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<h1><strong class="pkg">GUAVA</strong></h1>


<h2>A <strong class="pkg">GAP</strong>4 Package for computing with error-correcting codes  </h2>

<p>Version 3.20</p>

<p>1 February 2025</p>

</div>
<p><b>
Jasper Cramwinckel
</b>
</p><p><b>
Erik Roijackers
</b>
</p><p><b>
Reinald Baart
</b>
</p><p><b>
Eric Minkes
</b>
</p><p><b>
Lea Ruscio
</b>
</p><p><b>
Robert L Miller
</b>
</p><p><b>
Tom Boothby
</b>
</p><p><b>
Cen (``CJ'') Tjhai 
</b>
</p><p><b>
David Joyner                  

</b>
</p><p><b>
Joe Fields (Maintainer)   
    
     
    
</b>
<br />Email: <span class="URL"><a href="mailto:fieldsj1@southernct.edu">fieldsj1@southernct.edu</a></span>
<br />Homepage: <span class="URL"><a href="http://giam.southernct.edu/">http://giam.southernct.edu/</a></span>
<br />Address: <br />Mathematics Department,<br /> Southern Connecticut State University,<br /> New Haven, CT,<br /> 06515 USA.
</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p><strong class="pkg">GUAVA</strong>: © The GUAVA Group: 1992-2003 Jasper Cramwinckel, Erik Roijackers,Reinald Baart, Eric Minkes, Lea Ruscio (for the tex version), Jeffrey Leon © 2004 David Joyner, Cen Tjhai, Jasper Cramwinckel, Erik Roijackers, Reinald Baart, Eric Minkes, Lea Ruscio. © 2007 Robert L Miller, Tom Boothby © 2009, 2012, 2016, 2018, 2022, 2025 Joe Fields</p>

<p><strong class="pkg">GUAVA</strong> is released under the GNU General Public License (GPL).</p>

<p><strong class="pkg">GUAVA</strong> is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.</p>

<p><strong class="pkg">GUAVA</strong> is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.</p>

<p>You should have received a copy of the GNU General Public License along with <strong class="pkg">GUAVA</strong>; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA</p>

<p>For more details, see <span class="URL"><a href="https://www.fsf.org/licenses/gpl.html">https://www.fsf.org/licenses/gpl.html</a></span>.</p>

<p>For many years <strong class="pkg">GUAVA</strong> has been released along with the ``backtracking'' C programs of J. Leon. In one of his *.c files the following statements occur: ``Copyright (C) 1992 by Jeffrey S. Leon. This software may be used freely for educational and research purposes. Any other use requires permission from the author.'' The following should now be appended: ``I, Jeffrey S. Leon, agree to license all the partition backtrack code which I have written under the GPL (www.fsf.org) as of this date, April 17, 2007.''</p>

<p><strong class="pkg">GUAVA</strong> documentation: © Jasper Cramwinckel, Erik Roijackers, Reinald Baart, Eric Minkes, Lea Ruscio (for the tex version), Joe Fields, David Joyner, Cen Tjhai. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".</p>

<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p><strong class="pkg">GUAVA</strong> was originally written by Jasper Cramwinckel, Erik Roijackers, and Reinald Baart in the early-to-mid 1990's as a final project during their study of Mathematics at the Delft University of Technology, Department of Pure Mathematics, under the direction of Professor Juriaan Simonis. This work was continued in Aachen, at Lehrstuhl D fur Mathematik. In version 1.3, new functions were added by Eric Minkes, also from Delft University of Technology.



<p>JC, ER and RB would like to thank the GAP people at the RWTH Aachen for their support, A.E. Brouwer for his advice and J. Simonis for his supervision.</p>

<p>The GAP 4 version of <strong class="pkg">GUAVA</strong> (versions 1.4 and 1.5) was created by Lea Ruscio and (from 2001, starting with version 1.6, to early 2009) was maintained by David Joyner, who (with the help of several students) added several new functions. Starting with version 2.7, the ``best linear code'' tables for binary codes have been updated. From 2009, starting with version 3.10, <strong class="pkg">GUAVA</strong> has been maintained by Joe Fields. For further details, see the CHANGES file in the <strong class="pkg">GUAVA</strong> directory, also available at <span class="URL"><a href="https://gap-packages.github.io/guava/CHANGES.guava">https://gap-packages.github.io/guava/CHANGES.guava</a></span>.</p>

<p>This documentation was prepared with the <strong class="pkg">GAPDoc</strong> package of Frank Lübeck and Max Neunhöffer. The conversion from TeX to <strong class="pkg">GAPDoc</strong>'s XML was done by David Joyner in 2004.



<p>Please send bug reports, suggestions and other comments about <strong class="pkg">GUAVA</strong> to <span class="URL"><a href="mailto:support@gap-system.org">support@gap-system.org</a></span>. Currently known bugs and suggested <strong class="pkg">GUAVA</strong> projects are listed in the Issues section of the <strong class="pkg">GUAVA</strong> GitHub page: <span class="URL"><a href="https://github.com/gap-packages/guava/issues">https://github.com/gap-packages/guava/issues</a></span>. Older releases and further history can be found on the <strong class="pkg">GUAVA</strong> web page <span class="URL"><a href="https://gap-packages.github.io/guava/">https://gap-packages.github.io/guava/</a></span>.</p>

<p><em>Contributors</em>: Other than the authors listed on the title page, the following people have contributed code to the <strong class="pkg">GUAVA</strong> project: Alexander Hulpke, Steve Linton, Frank Lübeck, Aron Foster, Wayne Irons, Clifton (Clipper) Lennon, Jason McGowan, Shuhong Gao, Greg Gamble and Jeffrey S. Leon.</p>

<p>For documentation on Leon's programs, see the src/leon/doc subdirectory of GUAVA.



<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1_mj.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X787D826579603719">1.1 <span class="Heading">Introduction to the <strong class="pkg">GUAVA</strong> package</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7E2CB7DF83B514A8">1.2 <span class="Heading">Installing <strong class="pkg">GUAVA</strong></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X80EAA631863F805B">1.3 <span class="Heading">Loading <strong class="pkg">GUAVA</strong></span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X81904A7583751067">2 <span class="Heading">A First Tutorial in <strong class="pkg">GUAVA</strong></span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7B4C487180E9CBCD">2.1 <span class="Heading">Working with codewords</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7DEC2B677A1F2B03">2.2 <span class="Heading">Calculations with codes</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap3_mj.html#X836BAA9A7EBD08B1">3 <span class="Heading">Codewords</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X81B73ABB87DA8E49">3.1 <span class="Heading">Construction of Codewords</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B9E353D852851AA">3.1-1 Codeword</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7E7ED91C79BF3EF3">3.1-2 CodewordNr</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7F25479781E6E109">3.1-3 IsCodeword</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X8253374284B475B6">3.2 <span class="Heading">Comparisons of Codewords</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X82D4BC7380741DAE"><code>3.2-1 \=</code></a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7ADE7E95867A14E1">3.3 <span class="Heading">Arithmetic Operations for Codewords</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X84BD38C87F3956FB"><code>3.3-1 \+</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8692958781AF6CA8"><code>3.3-2 \-</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X86DC36217EC11723"><code>3.3-3 \+</code></a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7BBA5DCD7A8BD60D">3.4 <span class="Heading">
Functions that Convert Codewords to Vectors or Polynomials
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X87C8B0B178496F6A">3.4-1 VectorCodeword</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X822465E884D0F484">3.4-2 PolyCodeword</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X81D3230A797FE6E3">3.5 <span class="Heading">
Functions that Change the Display Form of a Codeword
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7E3E174B7954AA6B">3.5-1 TreatAsVector</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A6828148490BD2E">3.5-2 TreatAsPoly</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X805BF7147C68CACD">3.6 <span class="Heading">
Other Codeword Functions
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8000B6597EF0282F">3.6-1 NullWord</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7CDA1B547D55E6FB">3.6-2 DistanceCodeword</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B689C0284AC4296">3.6-3 Support</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7AD61C237D8D3849">3.6-4 WeightCodeword</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4_mj.html#X85FDDF0B7B7D87FB">4 <span class="Heading">Codes</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7ECE60E1873B49A6">4.1 <span class="Heading">Comparisons of Codes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8686D5FA839F1A3D"><code>4.1-1 \=</code></a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X832DA51986A3882C">4.2 <span class="Heading">
Operations for Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X82E2E5127CD25168"><code>4.2-1 \+</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7EFA08EE7BA22261"><code>4.2-2 \*</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X84D8B18F7C494A58"><code>4.2-3 \*</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8744BA5E78BCF3F9">4.2-4 InformationWord</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X864091AA7D4AFE86">4.3 <span class="Heading">
Boolean Functions for Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X87BDB89B7AAFE8AD">4.3-1 in</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X79CA175481F8105F">4.3-2 IsSubset</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7F71186281DEA83A">4.3-3 IsCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7B24748A7CE8D4B9">4.3-4 IsLinearCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X850C23D07C9A9B19">4.3-5 IsCyclicCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X85E3BD26856424F7">4.3-6 IsPerfectCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X789380D28018EC3F">4.3-7 IsMDSCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X80166D8D837FEB58">4.3-8 IsSelfDualCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7B2A0CC481D2366F">4.3-9 IsSelfOrthogonalCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8358D43981EBE970">4.3-10 IsDoublyEvenCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X79ACAEF5865414A0">4.3-11 IsSinglyEvenCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7CE150ED7C3DC455">4.3-12 IsEvenCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7B6DB8CC84FCAC1C">4.3-13 IsSelfComplementaryCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7AFD3844859B20BF">4.3-14 IsAffineCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X861D32FB81EF0D77">4.3-15 IsAlmostAffineCode</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X86442DCD7A0B2146">4.4 <span class="Heading">
Equivalence and Isomorphism of Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X843034687D9C75B0">4.4-1 IsEquivalent</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X874DED8E86BC180B">4.4-2 CodeIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X87677B0787B4461A">4.4-3 AutomorphismGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X79F3261F86C29F6D">4.4-4 PermutationAutomorphismGroup</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X866EB39483DDAE72">4.5 <span class="Heading">
Domain Functions for Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X808A4061809A6E67">4.5-1 IsFinite</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X858ADA3B7A684421">4.5-2 Size</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X86F070E0807DC34E">4.5-3 LeftActingDomain</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7E6926C6850E7C4E">4.5-4 Dimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X856D927378C33548">4.5-5 AsSSortedList</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X823827927D6A8235">4.6 <span class="Heading">
Printing and Displaying Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7AFA64D97A1F39A3">4.6-1 Print</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X81FB5BE27903EC32">4.6-2 String</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X83A5C59278E13248">4.6-3 Display</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7CD08C8C780543C4">4.6-4 DisplayBoundsInfo</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7D0F48B685A3ECDD">4.7 <span class="Heading">
Generating (Check) Matrices and Polynomials
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X817224657C9829C4">4.7-1 GeneratorMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X85D4B26E7FB38D57">4.7-2 CheckMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X78E33C3A843B0261">4.7-3 GeneratorPol</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7C45AA317BB1195F">4.7-4 CheckPol</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7F4CB9DB7CD97178">4.7-5 RootsOfCode</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X8170B52D7C154247">4.8 <span class="Heading">
Parameters of Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7A36C3C67B0062E8">4.8-1 WordLength</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7E33FD56792DBF3D">4.8-2 Redundancy</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7B31613D8538BD29">4.8-3 MinimumDistance</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X813F226F855590EE">4.8-4 MinimumDistanceLeon</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X84EDF67B86B4154C">4.8-5 MinimumWeight</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X823B9A797EE42F6D">4.8-6 DecreaseMinimumDistanceUpperBound</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7A679B0A7816B030">4.8-7 MinimumDistanceRandom</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7A195E317D2AB7CE">4.8-8 CoveringRadius</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X81004B007EC5DF58">4.8-9 SetCoveringRadius</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X806384B4815EFF2E">4.9 <span class="Heading">
Distributions
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7AEE64467FB1E0B9">4.9-1 MinimumWeightWords</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8728BCC9842A6E5D">4.9-2 WeightDistribution</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X871FD301820717A4">4.9-3 InnerDistribution</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X87AD54F87C5EE77E">4.9-4 DistancesDistribution</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8495870687195324">4.9-5 OuterDistribution</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7D9A39BF801948C8">4.10 <span class="Heading">
Decoding Functions
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7A42FF7D87FC34AC">4.10-1 Decode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7D870C9387C47D9F">4.10-2 Decodeword</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7D48DE2A84474C6A">4.10-3 GeneralizedReedSolomonDecoderGao</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7CFF98D483502053">4.10-4 GeneralizedReedSolomonListDecoder</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X80E17FA27DCAB676">4.10-5 BitFlipDecoder</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7B88DEB37F28404A">4.10-6 NearestNeighborGRSDecodewords</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X825E35757D778787">4.10-7 NearestNeighborDecodewords</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7D02E0FE8735D3E6">4.10-8 Syndrome</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7B9E71987E4294A7">4.10-9 SyndromeTable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8642D0BD789DA9B5">4.10-10 StandardArray</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X83231E717CCB0247">4.10-11 PermutationDecode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X85B692177E2A745D">4.10-12 PermutationDecodeNC</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap5_mj.html#X87EB64ED831CCE99">5 <span class="Heading">Generating Codes</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X86A92CB184CBD3C7">5.1 <span class="Heading">
Generating Unrestricted Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X81AACBDD86E89D7D">5.1-1 ElementsCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X86755AAC83A0AF4B">5.1-2 HadamardCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8122BA417F705997">5.1-3 ConferenceCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X81B7EE4279398F67">5.1-4 MOLSCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7D87DD6380B2CE69">5.1-5 RandomCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X816353397F25B62E">5.1-6 NordstromRobinsonCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7880D34485C60BAF">5.1-7 GreedyCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7C1B374583AFB923">5.1-8 LexiCode</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7A11F29F7BBF45BB">5.2 <span class="Heading">
Generating Linear Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X83F400A681CFC0D6">5.2-1 GeneratorMatCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7CDDDFE47A10A008">5.2-2 CheckMatCodeMutable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X848D3F7B805DEB66">5.2-3 CheckMatCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7DECB0A57C798583">5.2-4 HammingCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X801C88D578DA6ACA">5.2-5 ReedMullerCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X851592C7811D3D2A">5.2-6 AlternantCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7EE808BB7D1E487A">5.2-7 GoppaCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7F9C0A727EE075B7">5.2-8 GeneralizedSrivastavaCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7A38EB3178961F3E">5.2-9 SrivastavaCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X87F7CB8B7A8BE624">5.2-10 CordaroWagnerCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X865534267C8E902A">5.2-11 FerreroDesignCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7BCA10CE8660357F">5.2-12 RandomLinearCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X839CFE4C7A567D4D">5.2-13 OptimalityCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X871508567CB34D96">5.2-14 BestKnownLinearCode</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X858721967BE44000">5.3 <span class="Heading">
Gabidulin Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X79BE5D497CB2E59E">5.3-1 GabidulinCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X873950F67D4A9184">5.3-2 EnlargedGabidulinCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7F5BE77B7F343182">5.3-3 DavydovCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X845B4DBE83288D2D">5.3-4 TombakCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7D6583347C0D4292">5.3-5 EnlargedTombakCode</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X81F6E4A785F368B0">5.4 <span class="Heading">
Golay Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X80ED89C079CD0D09">5.4-1 BinaryGolayCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X84520C7983538806">5.4-2 ExtendedBinaryGolayCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7E0CCCD7866ADB94">5.4-3 TernaryGolayCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X81088A66816BCAE4">5.4-4 ExtendedTernaryGolayCode</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X8366CC3685F0BC85">5.5 <span class="Heading">
Generating Cyclic Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X853D34A5796CEB73">5.5-1 GeneratorPolCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X82440B78845F7F6E">5.5-2 CheckPolCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X818F0E6583E01D4B">5.5-3 RootsCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7C6BB07C87853C00">5.5-4 BCHCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X838F3CB3872CEF95">5.5-5 ReedSolomonCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8730B90A862A3B3E">5.5-6 ExtendedReedSolomonCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X825F42F68179D2AB">5.5-7 QRCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8764ABCF854C695E">5.5-8 QQRCodeNC</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7F4C3AD2795A8D7A">5.5-9 QQRCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7F3B8CC8831DA0E4">5.5-10 FireCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7BC245E37EB7B23F">5.5-11 WholeSpaceCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7B4EF2017B2C61AD">5.5-12 NullCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X83C5F8FE7827EAA7">5.5-13 RepetitionCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X82FA9F65854D98A6">5.5-14 CyclicCodes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8263CE4A790D294A">5.5-15 NrCyclicCodes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X79826B16785E8BD3">5.5-16 QuasiCyclicCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7BFEDA52835A601D">5.5-17 CyclicMDSCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7F40AF3B81C252DC">5.5-18 FourNegacirculantSelfDualCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X87137A257E761291">5.5-19 FourNegacirculantSelfDualCodeNC</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X850A28C579137220">5.6 <span class="Heading">
Evaluation Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X78E078567D19D433">5.6-1 EvaluationCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X810AB3DB844FFCE9">5.6-2 GeneralizedReedSolomonCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X85B8699680B9D786">5.6-3 GeneralizedReedMullerCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7EE68B58872D7E82">5.6-4 ToricPoints</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7B24BE418010F596">5.6-5 ToricCode</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7AE2B2CD7C647990">5.7 <span class="Heading">
Algebraic geometric codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X802DD9FB79A9ACA7">5.7-1 AffineCurve</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X857EFE567C05C981">5.7-2 AffinePointsOnCurve</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X857E36ED814A40B8">5.7-3 GenusCurve</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8572A3037DA66F88">5.7-4 GOrbitPoint </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X79742B7183051D99">5.7-5 DivisorOnAffineCurve</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8626E2B57D01F2DC">5.7-6 DivisorAddition </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X865FE28D828C1EAD">5.7-7 DivisorDegree </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X789DC358819A8F54">5.7-8 DivisorNegate </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8688C0E187B5C7DB">5.7-9 DivisorIsZero </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X816A07997D9A7075">5.7-10 DivisorsEqual </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X857B89847A649A26">5.7-11 DivisorGCD </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X82231CF08073695F">5.7-12 DivisorLCM </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X79C878697F99A10F">5.7-13 RiemannRochSpaceBasisFunctionP1 </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X856DDA207EDDF256">5.7-14 DivisorOfRationalFunctionP1 </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X878970A17E580224">5.7-15 RiemannRochSpaceBasisP1 </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X807C52E67A440DEB">5.7-16 MoebiusTransformation </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X85A0419580ED0391">5.7-17 ActionMoebiusTransformationOnFunction </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7E48F9C67E7FB7B5">5.7-18 ActionMoebiusTransformationOnDivisorP1 </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X79FD980E7B24DB9C">5.7-19 IsActionMoebiusTransformationOnDivisorDefinedP1 </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X823386037F450B0E">5.7-20 DivisorAutomorphismGroupP1 </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X80EDF3D682E7EF3F">5.7-21 MatrixRepresentationOnRiemannRochSpaceP1 </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8777388C7885E335">5.7-22 GoppaCodeClassical</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8422A310854C09B0">5.7-23 EvaluationBivariateCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7B6C2BED8319C811">5.7-24 EvaluationBivariateCodeNC</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X842E227E8785168E">5.7-25 OnePointAGCode</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X84F3673D7BBF5956">5.8 <span class="Heading">
Low-Density Parity-Check Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8020A9357AD0BA92">5.8-1 QCLDPCCodeFromGroup</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap6_mj.html#X866FC1117814B64D">6 <span class="Heading">Manipulating Codes</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X8271A4697FDA97B2">6.1 <span class="Heading">
Functions that Generate a New Code from a Given Code
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X794679BE7F9EB5C1">6.1-1 ExtendedCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7E6E4DDA79574FDB">6.1-2 PuncturedCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X87691AB67FF5621B">6.1-3 EvenWeightSubcode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X79577EB27BE8524B">6.1-4 PermutedCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X87E5849784BC60D2">6.1-5 ExpurgatedCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X8134BE2B8478BE8A">6.1-6 AugmentedCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7B0A6E1F82686B43">6.1-7 RemovedElementsCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X784E1255874FCA8A">6.1-8 AddedElementsCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X81CBEAFF7B9DE6EF">6.1-9 ShortenedCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7A5D5419846FC867">6.1-10 LengthenedCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7982D699803ECD0F">6.1-11 SubCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X809376187C1525AA">6.1-12 ResidueCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7E92DC9581F96594">6.1-13 ConstructionBCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X799B12F085ACB609">6.1-14 DualCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X81FE1F387DFCCB22">6.1-15 ConversionFieldCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X82D18907800FE3D9">6.1-16 TraceCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X8799F4BF81B0842B">6.1-17 CosetCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X873EA5EE85699832">6.1-18 ConstantWeightSubcode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7AA203A380BC4C79">6.1-19 StandardFormCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7EF49A257D6DB53B">6.1-20 PiecewiseConstantCode</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X7964BF0081CC8352">6.2 <span class="Heading">
Functions that Generate a New Code from Two or More Given Codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X79E00D3A8367D65A">6.2-1 DirectSumCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X86E9D6DE7F1A07E6">6.2-2 UUVCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7BFBBA5784C293C1">6.2-3 DirectProductCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X78F0B1BC81FB109C">6.2-4 IntersectionCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X8228A1F57A29B8F4">6.2-5 UnionCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7A85F8AF8154D387">6.2-6 ExtendedDirectSumCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7E17107686A845DB">6.2-7 AmalgamatedDirectSumCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7D8981AF7DFE9814">6.2-8 BlockwiseDirectSumCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7C37D467791CE99B">6.2-9 ConstructionXCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7B50943B8014134F">6.2-10 ConstructionXXCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X790C614985BFAE16">6.2-11 BZCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X820327D6854A50B5">6.2-12 BZCodeNC</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap7_mj.html#X7A814D518460862E">7 <span class="Heading">
Bounds on codes, special matrices and miscellaneous functions
</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X87C753EB840C34D3">7.1 <span class="Heading">
Distance bounds on codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8673277C7F6C04C3">7.1-1 UpperBoundSingleton</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X828095537C91FDFA">7.1-2 UpperBoundHamming</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X82EBFAAB7F5BFD4A">7.1-3 UpperBoundJohnson</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7A26E2537DFF4409">7.1-4 UpperBoundPlotkin</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X86A5A7C67F625A40">7.1-5 UpperBoundElias</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X82366C277E218130">7.1-6 UpperBoundGriesmer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8301FA9F7C6C7445">7.1-7 IsGriesmerCode</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7A5CB74485184FEE">7.1-8 UpperBound</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7FDF54BA81115D88">7.1-9 LowerBoundMinimumDistance</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7CF15D2084499869">7.1-10 LowerBoundGilbertVarshamov</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8217D830871286D8">7.1-11 LowerBoundSpherePacking</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7C6A58327BD6B685">7.1-12 UpperBoundMinimumDistance</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7B3858B27A9E509A">7.1-13 BoundsMinimumDistance</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X817D0A647D3331EB">7.2 <span class="Heading">
Covering radius bounds on codes
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8320D1C180A1AAAD">7.2-1 BoundsCoveringRadius</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7881E03E812140F4">7.2-2 IncreaseCoveringRadiusLowerBound</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7AD9F1D27C52BC0F">7.2-3 ExhaustiveSearchCoveringRadius</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X85D671F4824B4B0C">7.2-4 GeneralLowerBoundCoveringRadius</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8638F5A67D6E50C1">7.2-5 GeneralUpperBoundCoveringRadius</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7E7FBCC87D5562AB">7.2-6 LowerBoundCoveringRadiusSphereCovering</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X85E20C518360AB70">7.2-7 LowerBoundCoveringRadiusVanWee1</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7C72994A825228E7">7.2-8 LowerBoundCoveringRadiusVanWee2</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7F95362485759ACB">7.2-9 LowerBoundCoveringRadiusCountingExcess</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X829C14A383B5BF59">7.2-10 LowerBoundCoveringRadiusEmbedded1</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7B0C81B88604C448">7.2-11 LowerBoundCoveringRadiusEmbedded2</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7D27F6E27B9A0D35">7.2-12 LowerBoundCoveringRadiusInduction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X80F8DFAD7D67CBEC">7.2-13 UpperBoundCoveringRadiusRedundancy</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X832847A17FD0D142">7.2-14 UpperBoundCoveringRadiusDelsarte</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X86F10D9E79AB8796">7.2-15 UpperBoundCoveringRadiusStrength</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8585C6A982489FC3">7.2-16 UpperBoundCoveringRadiusGriesmerLike</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X82A38F5F858CF3FC">7.2-17 UpperBoundCoveringRadiusCyclicCode</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X806EBEC77C16E657">7.3 <span class="Heading">
Special matrices in <strong class="pkg">GUAVA</strong>
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X82899B64802A4BCE">7.3-1 KrawtchoukMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X87AFE2C078031CE4">7.3-2 GrayMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7E1E7C5287919CDB">7.3-3 SylvesterMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8014A1F181ECD8AA">7.3-4 HadamardMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X797F43607AD8660D">7.3-5 VandermondeMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7B47D82485B66F1D">7.3-6 PutStandardForm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7D4EDA0A854EBFEF">7.3-7 IsInStandardForm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7A97AD477E7638DE">7.3-8 PermutedCols</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7B68119F85E9EC6D">7.3-9 VerticalConversionFieldMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8033E9A67BA155C8">7.3-10 HorizontalConversionFieldMat</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X804AAFF2867080F7">7.3-11 MOLS</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7F34306B81DC2776">7.3-12 IsLatinSquare</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X81B9B40B7B2D97D5">7.3-13 AreMOLS</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X7AB5E5CE7FDF7132">7.4 <span class="Heading">
Some functions related to the norm of a code
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8032E53078264ABB">7.4-1 CoordinateNorm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7ED2EF368203AF47">7.4-2 CodeNorm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7D24F8BF7F9A7BF1">7.4-3 IsCoordinateAcceptable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X87039FD179AD3009">7.4-4 GeneralizedCodeNorm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X80283A2F7C8101BD">7.4-5 IsNormalCode</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X8308D685809A4E2F">7.5 <span class="Heading">
Miscellaneous functions
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X871286437DE7A6A4">7.5-1 CodeWeightEnumerator</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X84DA928083B103A0">7.5-2 CodeDistanceEnumerator</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X84B2BE66780EFBF9">7.5-3 CodeMacWilliamsTransform</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7903286078F8051B">7.5-4 CodeDensity</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X85303BAE7BD46D81">7.5-5 SphereContent</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7ACDC5377CD17451">7.5-6 Krawtchouk</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X827E39957A87EB51">7.5-7 PrimitiveUnityRoot</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X78AEA40F7AD9D541">7.5-8 PrimitivePolynomialsNr</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7A2B54EF868AA752">7.5-9 IrreduciblePolynomialsNr</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7B50D3417F6FD7C6">7.5-10 MatrixRepresentationOfElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7805D2BB7CE4D455">7.5-11 ReciprocalPolynomial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7AEA9F807E6FFEFF">7.5-12 CyclotomicCosets</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7A4EA98D794CF410">7.5-13 WeightHistogram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X805DF25C84585FD6">7.5-14 MultiplicityInList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8072B0DA78FBE562">7.5-15 MostCommonInList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7C5407EF87849857">7.5-16 RotateList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X85E526367878F72A">7.5-17 CirculantMatrix</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X7969103F7A8598F9">7.6 <span class="Heading">
Miscellaneous polynomial functions
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X84D51EBB784E7C5D">7.6-1 MatrixTransformationOnMultivariatePolynomial </a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X80433A4B792880EF">7.6-2 DegreeMultivariatePolynomial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X83F44E397C56F2E0">7.6-3 DegreesMultivariatePolynomial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X79E76B6F7D177E27">7.6-4 SolveLinearSystem</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X80171AA687FFDC70">7.6-5 GuavaVersion</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7EBBE86D85CC90C0">7.6-6 ZechLog</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X7C8C1E6A7E3497F0">7.6-7 CoefficientToPolynomial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X8431985183B63BB7">7.6-8 DegreesMonomialTerm</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7_mj.html#X860EF39B841380A1">7.6-9 DivisorsMultivariatePolynomial</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap8_mj.html#X7A93308C82637F4F">8 <span class="Heading">Coding theory functions in GAP</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X80F192497C008691">8.1 <span class="Heading">
Distance functions
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X82E5987E81487D18">8.1-1 AClosestVectorCombinationsMatFFEVecFFE</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X870DE258833C5AA0">8.1-2 AClosestVectorComb..MatFFEVecFFECoords</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X85135CEB86E61D49">8.1-3 DistancesDistributionMatFFEVecFFE</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X7F2F630984A9D3D6">8.1-4 DistancesDistributionVecFFEsVecFFE</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X7C9F4D657F9BA5A1">8.1-5 WeightVecFFE</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X85AA5C6587559C1C">8.1-6 DistanceVecFFE</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X87C3D1B984960984">8.2 <span class="Heading">
Other functions
</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X7C2425A786F09054">8.2-1 ConwayPolynomial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X7ECC593583E68A6C">8.2-2 RandomPrimitivePolynomial</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap9_mj.html#X82257DE97D1822AA">9 <span class="Heading">
GNU Free Documentation License
</span></a>
</div>
<div class="ContChap"><a href="chapBib_mj.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></div>
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