关键词: 自对偶码, 生成矩阵, 自同构, 等价

Abstract:

We discuss the binary selfdual codes of length 76 and 100 with automorphism of order 19. These binary selfdual codes can be seen as a direct sum of contract code of length 4 and some evenweight polynomials over  GF(2)n. We prove that selfdual codes of length between 80 and 100 do not exist. We also construct the binary selfdual codes of length 76, 78 and 80 through the shorter selfdual codes respectively, and present their generator matrices. Simulations in Matlab prove that under the condition of equivalence, there are 11 binary selfdual codes of 19(4, 2) and 19(4,4) types, whereas binary selfdual codes of 19(4, 0) type do not exist.

Key words: self-dual codes;generator matrix;automorphism;equivalence