有19-(4,f)型自同构的二元自对偶码

Binary self-dual codes with 19-(4,f)automorphism

应用二元自对偶码可看成几个自对偶码的直和理论,研究了具有19-(4,f)型自同构、码长在100以内的的二元自对偶码。这种对偶码都可看成一个码长为4的收缩码和GF(2)n上一些偶重量多项式的直和。证明了码长大于80且小于100时,不存在19-(4,f)型的二元自对偶码。根据码长较短的自对偶码分别构造出了码长为76、78和80的二元自对偶码,并给出其生成矩阵。由码的等价得到了这几类码可能的分类情况。运行Matlab程序,证明了具有19-(4,2)型和19-(4,4)型的二元自对偶码在等价情况下都有11个,19-(4,0)型的二元自对偶码在等价情况下是不存在的。

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 ex- ist. 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.