# even code

A binary code is called even if the Hamming weight of all its codewords is even. 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.

Title even code EvenCode 2013-03-22 15:15:42 2013-03-22 15:15:42 GrafZahl (9234) GrafZahl (9234) 4 GrafZahl (9234) Definition msc 94B05 LinearCode doubly-even code strictly even code