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%I #13 Jan 07 2019 05:55:05
%S 1,1,0,0,0,0,0,0,0,0,0,0,1,9,66,738,10760
%N Number of binary self-dual codes of length 2n having an automorphism group size that is a prime power.
%C Codes are vector spaces with a metric defined on them. Specifically, the metric is the hamming distance between two vectors. Vectors of a code are called codewords.
%C A code is usually represented by a generating matrix. The row space of the generating matrix is the code itself.
%C Self-dual codes are codes such all codewords are pairwise orthogonal to each other.
%C Two codes are called permutation equivalent if one code can be obtained by permuting the coordinates (columns) of the other code.
%C The automorphism group of a code is the set of permutations of the coordinates (columns) that result in the same identical code.
%C There are codes with a trivial automorphism group of size 1. This sequence does not count those codes.
%H W. Cary Huffman and Vera Pless, <a href="https://doi.org/10.1017/CBO9780511807077">Fundamentals of Error Correcting Codes</a>, 2003, pp. 7, 252-330, 338-393.
%e There are a(17)=10760 binary self-dual codes of length 2*17=34 having an automorphism group size that is a prime power.
%Y Cf. A322299, A322339, A322429.
%K nonn,more
%O 1,14
%A _Nathan J. Russell_, Dec 12 2018