cp's OEIS Frontend

A322309 Largest automorphism group size for a binary self-dual code of length 2n.

%I A322309 #12 Jul 23 2025 16:00:23
%S A322309 2,8,48,1344,3840,46080,645120,10321920,185794560,3715891200,
%T A322309 81749606400,1961990553600,51011754393600,1428329123020800,
%U A322309 42849873690624000,1371195958099968000,46620662575398912000
%N A322309 Largest automorphism group size for a binary self-dual code of length 2n.
%C A322309 A code is usually represented by a generating matrix.  The row space of the generating matrix is the code itself.
%C A322309 Self-dual codes are codes such that all codewords of the code are pairwise orthogonal to each other.
%C A322309 Two codes are called permutation equivalent if one code can be obtained by permuting the coordinates (columns) of the other code.
%C A322309 The automorphism group of a code is the set of permutations of the coordinates (columns) that result in the same identical code.
%C A322309 The values in the sequence are not calculated upper bounds.  For each n there exists a binary self-dual code of length 2n with an automorphism group of size a(n).
%C A322309 Binary self-dual codes have been classified (accounted for) up to a certain length. The classification process requires the automorphism group size be known for each code.  There is a mass formula to calculate the number of distinct binary self-dual codes of a given length.  The automorphism group size allows researchers to calculate the number of codes that are permutationally equivalent to a code.  Each new binary self-dual code C of length m that is discovered will account for m!/aut(C) codes in the total number calculated by the mass formula. Aut(C) represents the automorphism size of the code C.
%H A322309 W. Cary Huffman and Vera Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003, Pages 338-393.
%e A322309 The largest automorphism group size a binary self-dual code of length 2*16=32 is a(16) = 1371195958099968000.
%Y A322309 Cf. Self-Dual Codes A028362, A003179, A106162, A028363, A106163.
%K A322309 nonn
%O A322309 1,1
%A A322309 _Nathan J. Russell_, Dec 03 2018