cp's OEIS Frontend

The weight distribution list [w_0,w_1,...,w_30] = [1,0,0,6,0,53,0,339,0,1782,5284,0,8919,...,1] where w_i is the number of codewords of weight i, represents the most common weight distribution for the binary self-dual codes of length 2*15 = 30. There are a(15) = 16 binary self-dual codes that have this weight enumerator. Ellipses are used to shorten the list since the list is symmetrical (i.e., w_n = w_{30-n}).

The indexing of the list is 2n since there are no binary self-dual codes of odd length.

All binary self-dual codes of length 2*18 = 36 have a(9) = 131072 or fewer codewords with Hamming weight 18. In fact, there is only one binary self-dual code of length 36 that has 131072 codewords with Hamming weight 18.

There is at least one binary self-dual code of length 4n having a(n) codewords of weight 2n. However, the code may not be unique. There are two binary self-dual codes of length 4*4=16 having a(4)=198 codewords with Hamming weight 2*4=8.

All binary self-dual codes must be even length and all codewords must have an even Hamming weight. Only codewords with a length that is a multiple of 4 can have codewords with a Hamming weight equal to half the length of the code.