The OEIS is supported by the many generous donors to the OEIS Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323357 Number of binary self-dual codes of length 2n (up to permutation equivalence) that have a unique automorphism group size. 1
1, 1, 1, 2, 2, 3, 4, 7, 9, 16, 23, 42, 68, 94, 124, 159, 187, 212 (list; graph; refs; listen; history; text; internal format)
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.
W. Cary Huffman and Vera Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003, Pages 338-393.
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.
For self-dual codes see A028362, A003179, A106162, A028363, A106163, A269455, A120373; for automorphism groups see A322299, A322339.
Sequence in context: A110160 A277252 A241415 * A322299 A003179 A153934
Nathan J. Russell, Jan 12 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 19:10 EST 2023. Contains 367540 sequences. (Running on oeis4.)