A322073 Number of binary self-dual codes that share the most common weight distribution for binary self-dual codes of length 2n.

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 10, 16, 53, 553, 14536

Offset: 1

Author

Nathan J. Russell, Nov 25 2018

Keywords

• nonn
• more

Comments

The weight distribution list [w_0,w_1,...,w_30] = [1,0,0,6,0,53,0,339,0,1782,5284,0,8919,...,1] where w_i is the number of codewords of weight i, represents the most common weight distribution for the binary self-dual codes of length 2*15 = 30. There are a(15) = 16 binary self-dual codes that have this weight enumerator. Ellipses are used to shorten the list since the list is symmetrical (i.e., w_n = w_{30-n}).

The indexing of the list is 2n since there are no binary self-dual codes of odd length.

Links

• W. Cary Huffman and Vera Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003, Pages 7,252-282,338-393.

Crossrefs

Cf. A296086, A321969.