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<!DOCTYPE html> <html lang="en"> <head> <title>shorten -- shortens a code</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="tools for Coding Theory" href="index.html">CodingTheory</a> » <a title="class of linear codes" href="___Linear__Code.html">LinearCode</a> » <a title="functions to construct linear codes over Galois fields" href="_linear__Code.html">linearCode</a> » <a title="shortens a code" href="_shorten.html">shorten</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> <a href="_universe__Code.html">next</a> | <a href="_repetition__Code.html">previous</a> | <a href="_universe__Code.html">forward</a> | <a href="_repetition__Code.html">backward</a> | <a href="_linear__Code.html">up</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>shorten -- shortens a code</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">shorten(LinearCode, List)</code></dd> <dd><code class="language-macaulay2">shorten(LindearCode, ZZ)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">C</span>, <span>an instance of the type <a title="class of linear codes" href="___Linear__Code.html">LinearCode</a></span>, </span></li> <li><span><span class="tt">L</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, </span></li> <li><span><span class="tt">i</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, </span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>an instance of the type <a title="class of linear codes" href="___Linear__Code.html">LinearCode</a></span>, </span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>Given a code <span class="tt">C</span> of length $n$ and a list <span class="tt">L</span> (or an integer <span class="tt">i</span>), returns a new code obtained from <span class="tt">C</span> by selecting only those codewords of <span class="tt">C</span> that have zeros in each of the coordinate positions in the list <span class="tt">L</span> (or the position <span class="tt">i</span>), and then deleting these positions.</p> </div> <div> <p>The resulting code will have length $n - r$, where $r$ is the number of elements in <span class="tt">L</span> (or 1 when the integer <span class="tt">i</span> is used).</p> </div> <div> <h2>a code and a list are given</h2> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">shorten(LinearCode, List)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">C</span>, <span>an instance of the type <a title="class of linear codes" href="___Linear__Code.html">LinearCode</a></span>, </span></li> <li><span><span class="tt">L</span>, <span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, </span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>an instance of the type <a title="class of linear codes" href="___Linear__Code.html">LinearCode</a></span>, </span></li> </ul> </li> </ul> <div> <p>Given a code <span class="tt">C</span> of length $n$ and a list <span class="tt">L</span>, returns a new code obtained from <span class="tt">C</span> by selecting only those codewords of <span class="tt">C</span> that have zeros in each of the coordinate positions in the list <span class="tt">L</span>, and then deleting these positions.</p> </div> <div> <p>The resulting code will have length $n - r$, where $r$ is the number of elements in <span class="tt">L</span>.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : F = GF(2);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : codeLen = 10;</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : L = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 1, 0,0}, {1, 1, 0, 0, 0, 1, 0, 0, 1, 0}, {1, 0, 0, 1, 0, 0, 0, 1, 1,1}};</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i4 : C = linearCode(F,codeLen,L);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : shorten(C, {3,6,8,9});</code></pre> </td> </tr> </table> </div> <div> <h2>a linear code and an integer are given</h2> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">shorten(LinearCode, ZZ)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">C</span>, <span>an instance of the type <a title="class of linear codes" href="___Linear__Code.html">LinearCode</a></span>, </span></li> <li><span><span class="tt">i</span>, <span>an <a title="the class of all integers" href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, </span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>an instance of the type <a title="class of linear codes" href="___Linear__Code.html">LinearCode</a></span>, $C$</span></li> </ul> </li> </ul> <div> <p>Given a code <span class="tt">C</span> of length $n$ and a list <span class="tt">L</span>, returns a new code obtained from <span class="tt">C</span> by selecting only those codewords of <span class="tt">C</span> that have zero in the position <span class="tt">i</span>), and then deleting this position.</p> </div> <div> <p>The resulting code will have length $n - 1$.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i6 : F = GF(2);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i7 : codeLen = 10;</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : L = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 1, 0,0}, {1, 1, 0, 0, 0, 1, 0, 0, 1, 0}, {1, 0, 0, 1, 0, 0, 0, 1, 1,1}};</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i9 : C = linearCode(F,codeLen,L);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i10 : shorten(C, 3) 9 o10 = LinearCode{AmbientModule => F } BaseField => F cache => CacheTable{} Code => image | 0 1 1 1 0 0 1 0 | | 1 1 1 0 0 0 0 1 | | 0 0 1 1 1 0 0 1 | | 0 0 1 1 1 0 0 1 | | 0 1 0 0 1 0 1 1 | | 0 0 0 0 0 0 0 0 | | 0 0 1 1 1 0 0 1 | | 0 1 1 1 0 0 1 0 | | 0 0 0 0 0 0 0 0 | GeneratorMatrix => | 0 1 0 0 0 0 0 0 0 | | 1 1 0 0 1 0 0 1 0 | | 1 1 1 1 0 0 1 1 0 | | 1 0 1 1 0 0 1 1 0 | | 0 0 1 1 1 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 1 0 0 0 1 0 0 1 0 | | 0 1 1 1 1 0 1 0 0 | Generators => {{0, 1, 0, 0, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 1, 0, 0, 1, 0}, {1, 1, 1, 1, 0, 0, 1, 1, 0}, {1, 0, 1, 1, 0, 0, 1, 1, 0}, {0, 0, 1, 1, 1, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 1, 0, 0, 1, 0}, {0, 1, 1, 1, 1, 0, 1, 0, 0}} ParityCheckMatrix => | 0 0 1 1 0 0 0 0 0 | | 1 0 1 0 1 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 1 0 0 0 1 0 0 | | 1 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 1 | ParityCheckRows => {{0, 0, 1, 1, 0, 0, 0, 0, 0}, {1, 0, 1, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 1, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1}} o10 : LinearCode</code></pre> </td> </tr> </table> </div> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">shorten</span>:</h2> <ul> <li><kbd>shorten(LinearCode,List)</kbd></li> <li><kbd>shorten(LinearCode,ZZ)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="shortens a code" href="_shorten.html">shorten</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">CodingTheory.m2:3438:0</span>.</p> </div> </div> </div> </body> </html>