http://debianws.lexgopc.com/wiki143/index.php?action=history&feed=atom&title=Even_codeEven code - Revision history2026-05-05T22:31:39ZRevision history for this page on the wikiMediaWiki 1.43.1http://debianws.lexgopc.com/wiki143/index.php?title=Even_code&diff=2722597&oldid=previmported>Jlwoodwa: WP:STUBSPACING2024-04-29T18:33:33Z<p><a href="/wiki143/index.php?title=WP:STUBSPACING&action=edit&redlink=1" class="new" title="WP:STUBSPACING (page does not exist)">WP:STUBSPACING</a></p>
<p><b>New page</b></p><div>{{Short description|If the Hamming weight of all of a binary code's codewords is even}}<br />
{{One source|date=October 2023}}<br />
A [[linear code|binary code]] is called an '''even code''' if the [[Hamming weight]] of each of its codewords is even. An even code should have a generator polynomial that include (1+''x'') minimal polynomial as a product. Furthermore, a binary code is called '''doubly even''' if the Hamming weight of all its codewords is [[divisible by 4]]. An even code which is not doubly even is said to be strictly even.<br />
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Examples of doubly even codes are the extended binary [[Hamming code]] of block length 8 and the extended binary [[Binary Golay code|Golay code]] of block length 24. These two codes are, in addition, [[self-dual code|self-dual]].<br />
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{{PlanetMath attribution|id=7047|title=even code}}<br />
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[[Category:Coding theory]]<br />
[[Category:Parity (mathematics)]]<br />
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