A recursive enumeration of the inequivalent binary (2k,k) self-dual codes, or 2k less than or equal to 32

Abstract

A binary self-dual code of length 2k is a (2k, k) binary linear code C with the property that every pair of codewords in C are orthogonal. Two binary self-dual codes of equal length, $C\sb1$ and $C\sb2,$ are said to be equivalent if and only if there exists a permutation of the coordinates of $C\sb1$ that takes $C\sb1$ into $C\sb2.$ If $C\sb1$ and $C\sb2$ are not equivalent then $C\sb1$ and $C\sb2$ are said to be inequivalent. The automorphism group of a binary linear code C is the set of all permutations of the coordinates of C that takes C into itself. The main topic in this thesis is the enumeration of lists of inequivalent binary self-dual codes. We have developed algorithms that have allowed us to enumerate lists of inequivalent binary self-dual codes of lengths up to and including 32. This is the first time a list of inequivalent binary-self dual codes of length 32 has been enumerated. Our algorithms also find the size of the automorphism group of each code.