cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A322299 Number of distinct automorphism group sizes for binary self-dual codes of length 2n.

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%I A322299 #15 Jan 07 2019 05:55:27
%S A322299 1,1,1,2,2,3,4,7,9,16,24,48,85,149,245,388
%N A322299 Number of distinct automorphism group sizes for binary self-dual codes of length 2n.
%C A322299 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 A322299 A code is usually represented by a generating matrix.  The row space of the generating matrix is the code itself.
%C A322299 Self-dual codes are codes such all codewords are pairwise orthogonal to each other.
%C A322299 Two codes are called permutation equivalent if one code can be obtained by permuting the coordinates (columns) of the other code.
%C A322299 The automorphism group of a code is the set of permutations of the coordinates (columns) that result in the same identical code.
%H A322299 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 A322299 There are a(16) = 388 distinct sizes for the automorphism groups of the binary self-dual codes of length 16.  In general, two automorphism  groups with the same size are not necessarily isomorphic.
%Y A322299 Cf. self-dual codes A028362, A003179, A106162, A028363, A106163.
%K A322299 nonn,more
%O A322299 1,4
%A A322299 _Nathan J. Russell_, Dec 02 2018