A323358 Number of distinct automorphism group sizes for binary self-dual codes of length 2n such that multiple same length binary self-dual codes with different weight distributions share the same automorphism group size.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 17, 55, 117, 226, 343, 535

Offset: 1

Author

Nathan J. Russell, Jan 12 2019

Keywords

• nonn
• more
• hard

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 for a given length.

There are instances where more than one code can share the same automorphism group size yet have different weight distributions (weight enumerator). This sequence provides the number of automorphism group sizes where this is true for a given length.

Examples

			There are a(18) = 535 automorphism group sizes for the binary self-dual codes of length 2*18 = 36 where codes having different weight distributions share the same 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, A323357.