OFFSET
1,12
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.
LINKS
W. Cary Huffman and Vera Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003, Pages 338-393.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Nathan J. Russell, Jan 12 2019
STATUS
approved