A323357 Number of binary self-dual codes of length 2n (up to permutation equivalence) that have a unique automorphism group size.

1, 1, 1, 2, 2, 3, 4, 7, 9, 16, 23, 42, 68, 94, 124, 159, 187, 212

Offset: 1

Author

Nathan J. Russell, Jan 12 2019

Keywords

• nonn
• more

Comments

Two codes are said to be permutation equivalent if permuting the columns of one code results in the other code.

If permuting the columns of a code results in the same identical code the permutation is called an automorphism.

The automorphisms of a code form a group called the automorphism group.

Some codes have automorphism groups that contain the same number of elements. There are situations, both trivial and otherwise, that codes of different lengths can have the same size automorphism groups.

Some codes have automorphism group sizes that are unique to the code. This sequence only compares automorphism group sizes for codes with the same length.

Examples

			There are a(18) = 212 binary self-dual codes (up to permutation equivalence) of length 2*18 = 36 that have a unique automorphism group size.
		

Links

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

Crossrefs

For self-dual codes see A028362, A003179, A106162, A028363, A106163, A269455, A120373; for automorphism groups see A322299, A322339.