<p id
<p><<iv="chlinkprevnextbot[1 0, 0, 0,1]
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
lassContSectspanclasstocline> class""&;/>a hrefchap2#X7B4C487180E9CBCD1< "> with codewords/>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7DEC2B677A1F2B03">2.2 <span class="Heading">Calculations with codes</span></a>
</span
</>
</div>
<h3>2 <span class="Heading"java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<p>An error-correcting code is essentially just a subset of the set of all possible messages of a given length over some finite "alphabet."</p>
<p>In
<>Whenamessageis received that isnot codeword, we ask thequestionWhichcodeword closesttomessageI've eceived?" In words wemake the presumption that the received message is actually a codeword that has been changed in a relatively small number of positions -- and we put them back the way they were supposed to be!
<p>That [125,?] randomly generated codeover(2)
<p><a id
<h4p ="SimpleMath"n</span <span class="SimpleMath">k</ classSimpleMathdspan> ">n ( wordlength),and SimpleMath><span(the' dimension) aswell as serves s the alphabet the code.
<p>So let's play around a bit.
<p>Start <strong class="pkg">GAP</strong> in a terminal window, then issue the command</p>
<div class="example"><pre>
<span class="GAPprompt">gap
truep>One of the most features of a codeafeature that determines how goodit willbe correcting errors isits minimum weight, <spanclassSimpleMath><span.Thisis smallestweight any nonzero word in code. Ifwewishto correct<span class"">m</> errorswe will to have a minimum weight at least <spanclass"SimpleMath">+<span./>
<
<p><strong class="pkg">GUAVA</strong> can
<div class="example"><pre>
<spanclass"APprompt">></span> <span class="GAPinput">c1:=Codeword("10101011")</>
[1010 0101]
<span class="GAPprompt">gap></span> <span class="GAPinput">v:=Z(2)*[1,1,1,1,1,1,1,1,1];</span>
[()0,Z(2^0 Z(2)^0, Z(2)0, Z(2)^,Z(2^0,Z()^,Z2)0 Z2)0]
<span class="GAPprompt">gap></span> <span class="GAPinput">[1, 0,02, 3 6, 7, 6, 4, ,, 0,0 ]
[1111111 1]
<span class/pre></java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
0 0 10 0 java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
<< />
5
=="gap;/span "Weight)<span
9
<span ="GAPprompt"gap;/body>
4
</pre>< type<>
<pThe excerpt a < class=pkg</strongsession shows that codewords can constructed quoted orfromvectors whoseentries infinite.We see codewords beaddedtogether that is called class"Weight/> which (if isn't ) tells us how many entries in a codeword non-zero.
<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<p>Note that the Hamming distance between <code class="code">c1</code> and <code class="code">c2</code> happens to give the same value as the weight< ="X81904A7583751067 name"894"/p>
<p>Acodeword can be using . Indeed internal of codeword requires a polynomial a vector.There < class"">GUAVAstrong that one switch and between two.</pjava.lang.StringIndexOutOfBoundsException: Index 281 out of bounds for length 281
<<> <strong="pkg">GAP</strong> in a terminal window, then issue the command>
<p>A code is fundamentally just a collection of codewords. Sometimes a code is
<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<div class="example"><pre>
<span class=1 1 0 101]
< class"gapgt;/>span="">gap;<spanspan ="GAPinput>c1;/java.lang.StringIndexOutOfBoundsException: Index 80 out of bounds for length 80
[ 1 0,0 6 ,0 1]
<p></div
<p>In this example we first wrote out a list of strings, then converted them into codewords over GF(2). The
<p> very feature <strong="pkg>> the ability to construct random codes:
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">C:= RandomLinearCode(12,5,GF(2));</span>
a [12,5,?] randomly generated code over GF(2)
</pre></div>
<p>A codeword can be usingpolynomialIndeed, the internal ofcodeword requires either or a vectorThere <strong class="pkg"GUAVA> oneandthe<pjava.lang.StringIndexOutOfBoundsException: Index 281 out of bounds for length 281
<p> of most features a ( that how it be correcting) is minimum, <span="SimpleMath">d<span isthe weight any word the we to correct <span class="SimpleMath">m</span> errors we will need to have a minimum weight of at least <span class="SimpleMath">2m+1</span>.</p>
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.