even code

A binary code is called even if the Hamming weight of all itscodewords is even. Furthermore, a binary code is calleddoubly-even if the Hamming weight of all its codewords isdivisible by $4$. An even code which is not doubly-even is said to bestrictly even.

Examples of doubly-even codes are the extended binary Hamming code ofblock length $8$ and the extended binary Golay code of block length$24$. These two codes are, in addition, self-dual.