A321945 Number of binary self-dual codes of length 2n having an automorphism group size that is a prime power.

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 9, 66, 738, 10760

Offset: 1

Author

Nathan J. Russell, Dec 12 2018

Keywords

• nonn
• more

Comments

Codes are vector spaces with a metric defined on them. Specifically, the metric is the hamming distance between two vectors. Vectors of a code are called codewords.

A code is usually represented by a generating matrix. The row space of the generating matrix is the code itself.

Self-dual codes are codes such all codewords are pairwise orthogonal to each other.

Two codes are called permutation equivalent if one code can be obtained by permuting the coordinates (columns) of the other code.

The automorphism group of a code is the set of permutations of the coordinates (columns) that result in the same identical code.

There are codes with a trivial automorphism group of size 1. This sequence does not count those codes.

Examples

			There are a(17)=10760 binary self-dual codes of length 2*17=34 having an automorphism group size that is a prime power.
		

Links

• W. Cary Huffman and Vera Pless, Fundamentals of Error Correcting Codes, 2003, pp. 7, 252-330, 338-393.

Crossrefs

Cf. A322299, A322339, A322429.