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%I #24 Nov 01 2019 20:50:54
%S 2,14,32,198,512,2972,8192,45638,131072
%N Maximum number of codewords a binary self-dual code of length 4n can have with Hamming weight 2n (half of length).
%C 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.
%C 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.
%C 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.
%H W. Cary Huffman and Vera Pless, <a href="https://doi.org/10.1017/CBO9780511807077">Fundamentals of Error Correcting Codes</a>, 2003, Page 7, 252-330, 338-393.
%Y Cf. A322073, A321969, A296086, A001405, A000984.
%K nonn,more
%O 1,1
%A _Nathan J. Russell_, Nov 25 2018
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