Some optimal self-orthogonal and self-dual codes

Abstract

The binary optimal self-orthogonal codes of dimension 4≤k≤ 10 and length 15≤n≤k + 16 are classified. They are used for constructing self-dual codes of lengths 40, 42, and 44. All optimal binary self-dual codes of lengths 42 and 44 which have an automorphism of order 5 with four independent cycles are obtained up to equivalence. All optimal self-dual codes of lengths 40, 42 and 44 which have an automorphism of order 3 with six independent cycles are constructed. Some of them are the firstknown codes with their weight enumerators. © 2004 Elsevier B.V. All rights reserved.