Even code

{{Short description|If the Hamming weight of all of a binary code's codewords is even}} {{One source|date=October 2023}} A binary [[linear 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 includes the (''x''+1) 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 Golay code]] of block length 24. These two codes are, in addition, [[self-dual code|self-dual]].

[[Category:Coding theory]] [[Category:Parity (mathematics)]]