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<h1 >QDistRnd</h1 >
<h2>Calculate the distance of a q-ary quantum stabilizer code </h2>
<p>
0.9.5</p>
<p>
20 November 2024
</p>
</div >
<p><b>
Leonid P. Pryadko
</b>
<br />Email: <span class="URL" ><a href="mailto:leonid.pryadko@gmail.com" >leonid.pryadko@gmail.com</a></span >
<br />Homepage: <span class="URL" ><a href="http://faculty.ucr.edu/~leonid " >http://faculty.ucr.edu/~leonid</a></span >
<br />Address : <br />Department of Physics & Astronomy<br /> University of California<br /> Riverside, CA 92521<br /> USA<br />
</p><p><b>
V. A. Shabashov
</b>
<br />Email: <span class="URL" ><a href="mailto:vadim.art.shabashov@gmail.com" >vadim.art.shabashov@gmail.com</a></span >
<br />Homepage: <span class="URL" ><a href="https://sites.google.com/view/vadim-shabashov/ " >https://sites.google.com/view/vadim-shabashov/</a></span >
</p><p><b>
V. K. Kozin
</b>
<br />Email: <span class="URL" ><a href="mailto:kozin.valera@gmail.com" >kozin.valera@gmail.com</a></span >
<br />Address : <br />Department of Physics, University of Basel<br /> Klingelbergstrasse 82, CH-4056 Basel,<br /> Switzerland<br />
</p>
<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>
<h3>Copyright</h3>
<p>© 2021--2024 by L. P. Pryadko, V. K. Kozin, and V. A. Shabashov</p>
<p><strong class="pkg" >QDistRnd</strong > package is free software; you can redistribute it and/or modify it under the terms of the <span class="URL" ><a href="https://www.fsf.org/licenses/gpl.html " >GNU General Public License</a></span > as published by the Free Software Foundation; either version 2 of the License, or (at your option ) any later version.</p>
<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA" ></a></p>
<h3>Acknowledgements</h3>
<p>We appreciate very much all past and future comments, suggestions and contributions to this package and its documentation provided by <strong class="pkg" >GAP</strong > users and developers.</p>
<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.html#X7DFB63A97E67C0A1" >1 <span class="Heading" >Introduction</span ></a>
</div >
<div class="ContChap" ><a href="chap2.html#X7A489A5D79DA9E5C" >2 <span class="Heading" >Examples</span ></a>
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X7B229D2B7E58ED2E" >2.1 <span class="Heading" >The 5-qubit code </span ></a>
</span >
</div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X87244D1D7FAA03A1" >2.2 <span class="Heading" >Hyperbolic codes from a file</span ></a>
</span >
</div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap2.html#X7A1DF21D8626DA84" >2.3 <span class="Heading" >Randomly generated cyclic codes</span ></a>
</span >
</div >
</div >
<div class="ContChap" ><a href="chap3.html#X7E421FAB7D974939" >3 <span class="Heading" >Description of the algorithm</span ></a>
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X7DDF42DF7D7F87EF" >3.1 <span class="Heading" >Elementary version</span ></a>
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7AE39C5583A02936" >3.1-1 <span class="Heading" >What it does?</span ></a>
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7C198D417DA58DFD" >3.1-2 <span class="Heading" >The algorithm</span ></a>
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7C37FBD078DDC0D5" >3.1-3 <span class="Heading" >Intuition</span ></a>
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7A291E1E7CD313AB" >3.1-4 <span class="Heading" >CSS version of the algorithm</span ></a>
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7D97C75283D26EE5" >3.1-5 <span class="Heading" >Generic version of the algorithm</span ></a>
</span >
</div ></div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X7DA7BD6F7A61E553" >3.2 <span class="Heading" >Some more details </span ></a>
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X78810FD98017EB84" >3.2-1 <span class="Heading" >Quantum stabilizer codes</span ></a>
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7C198D417DA58DFD" >3.2-2 <span class="Heading" >The algorithm</span ></a>
</span >
</div ></div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X7CCA4B9B834960EE" >3.3 <span class="Heading" >Empirical estimate of the success probability</span ></a>
</span >
</div >
</div >
<div class="ContChap" ><a href="chap4.html#X7C6522597D7E72FE" >4 <span class="Heading" >All Functions</span ></a>
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X826856C47F9890F3" >4.1 <span class="Heading" >Functions for computing the distance</span ></a>
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X83CF58308216037F" >4.1-1 DistRandCSS</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7894F0027B144AB8" >4.1-2 DistRandStab</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7A489A5D79DA9E5C" >4.1-3 <span class="Heading" >Examples</span ></a>
</span >
</div ></div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X7E4EA2B38128F66B" >4.2 <span class="Heading" >Input /Output Functions</span ></a>
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X86210A658573655F" >4.2-1 ReadMTXE</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X82F72B6082EEDDF9" >4.2-2 WriteMTXE</a></span >
</div ></div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X7BD4785D8488BAD5" >4.3 <span class="Heading" >Helper Functions</span ></a>
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X80975EC07BDC757B" >4.3-1 QDR_AverageCalc</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8615F38C79B4684C" >4.3-2 QDR_SymplVecWeight</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X80BB67727F7F99C3" >4.3-3 QDR_WeightMat</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8441E8807AE9C477" >4.3-4 QDR_DoProbOut</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7B6713FC7A5124A8" >4.3-5 QDR_ParseFieldStr</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X810D9FD7796AD286" >4.3-6 QDR_ParsePolyStr</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8638277B86B97B56" >4.3-7 QDR_FieldHeaderStr</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8388DFBC816EF47D" >4.3-8 QDR_ProcessFieldHeader</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X82A75836794421A8" >4.3-9 QDR_ProcEntry</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7A489A5D79DA9E5C" >4.3-10 <span class="Heading" >Examples</span ></a>
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8020FCA787C830FE" >4.3-11 QDR_MakeH</a></span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X819DC3247F3F7B4F" >4.3-12 QDR_DoCirc</a></span >
</div ></div >
</div >
<div class="ContChap" ><a href="chap5.html#X7D0187B5831B764D" >5 <span class="Heading" >Extended MTX (MTXE) File Format</span ></a>
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X7E294E8678035D23" >5.1 <span class="Heading" >General information</span ></a>
</span >
<div class="ContSSBlock" >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X8269F2367856BB1E" >5.1-1 <span class="Heading" >Representation of field elements via integers</span ></a>
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X86FBB72C7BC3B8D2" >5.1-2 <span class="Heading" >Matrix storage format</span ></a>
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X80B886F0796AF0D5" >5.1-3 <span class="Heading" >Explicit format of each line</span ></a>
</span >
<span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X80F0F8AB7FD73B0E" >5.1-4 <span class="Heading" >Matrix Storage Implementation Details </span ></a>
</span >
</div ></div >
<div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X7F2C657F869D90AD" >5.2 <span class="Heading" >Example MTXE files</span ></a>
</span >
</div >
</div >
<div class="ContChap" ><a href="chapBib.html" ><span class="Heading" >References</span ></a></div >
<div class="ContChap" ><a href="chapInd.html" ><span class="Heading" >Index</span ></a></div >
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