Even code: Difference between revisions

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{{Short description|If the Hamming weight of all of a binary code's codewords is even}}

{{One source|date=October 2023}}

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.

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]].

{{PlanetMath attribution|id=7047|title=even code}}

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[[Category:Coding theory]]

[[Category:Parity (mathematics)]]

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