Even code

A binary code is called an even code if the Hamming weight of all 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 Golay code of block length 24. These two codes are, in addition, self-dual.

even code at PlanetMath.