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.
%I A321946 #11 Jan 07 2019 05:55:16 %S A321946 2,4,10,28,36,66,144,192,340,570,1200,1656,3456,5616,9072,10752,22176 %N A321946 Number of divisors for the automorphism group size having the largest number of divisors for a binary self-dual code of length 2n. %C A321946 A code is usually represented by a generating matrix. The row space of the generating matrix is the code itself. %C A321946 Self-dual codes are codes such all codewords are pairwise orthogonal to each other. %C A321946 Two codes are called permutation equivalent if one code can be obtained by permuting the coordinates (columns) of the other code. %C A321946 The automorphism group of a code is the set of permutations of the coordinates (columns) that result in the same identical code. %C A321946 The values in the sequence are not calculated lower bounds. For each n there exists a binary self-dual code of length 2n with an automorphism group of size a(n). %C A321946 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. Sequence A028362gives this count. 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. Sequence A003179 gives number of binary self-dual codes up to permutation equivalence. %C A321946 The values in the sequence are not calculated by a formula or algorithm. They are the result of calculating the number of divisors for every automorphism group of every binary self-dual code. %C A321946 The number of divisors a(n) does count 1 and the number itself. %C A321946 In general the automorphism group size with the largest number of divisors is not unique. %C A321946 In general the automorphism group size with the largest number of divisors is not the largest group automorphism group size for a given binary self-dual code length. %H A321946 W. Cary Huffman and Vera Pless, <a href="https://doi.org/10.1017/CBO9780511807077">Fundamentals of Error Correcting Codes</a>, Cambridge University Press, 2003, Pages 338-393. %e A321946 There is one binary self-dual code of length 2*14=28 having an automorphism group size of 1428329123020800. This number has a(14) = 5616 divisors (including 1 and 1428329123020800). The automorphism size of 1428329123020800 represents the automorphism size with the largest number of divisors for a binary self-dual code of length 2*14=28. %Y A321946 Cf. Self-Dual Codes A028362, A003179, A106162, A028363, A106163, A269455, A120373. %Y A321946 Cf. Self-Dual Code Automorphism Groups A322299, A322339. %K A321946 nonn,more %O A321946 1,1 %A A321946 _Nathan J. Russell_, Dec 12 2018