【摘要】 把长度为56的具有7-(8,0)型自同构的二元双偶极值码看成二元域上的多项式,分解成一个收缩码和一个偶重量多项式的直和。利用已知的码长较短的编码构造出长度为56的具有7-(8,0)型自同构的二元双偶极值码,并给出可能的生成矩阵。由于该双偶极值码的最小距离为12,根据两个码等价的类型,对生成矩阵运行Matlab程序,证明了在等价情况下,当E1(σ)*的维数K=2时,不存在有7-(8,0)型自同构的二元双偶极值码;当E1(σ)*的维数K=4时,有7-(8,0)型自同构二元双偶极值码共75种。对长度为56到70的具有类似型自同构的双偶极值码进行相似讨论,得到了其生成矩阵和分类情况。至此,长度在50到70之间的二元双偶极值码的生成矩阵和分类情况得到完全解决。更多还原

【Abstract】 By regarding the extremal self-dual doubly-even binary codes with type of 7-(8,0)as a polynomial over GF(2)n,we can factorize it to a contract code and even weight polynomials,and construct extremal self-dual doubly-even binary codes with type of 7-(8,0)by shorter codes.The possible generator matrix of the codes is given.Matlab procedure implementation shows that,because the minimal distance is 12,codes with type of 7-(8,0)do not exist when the dimension of E1(σ)*is 2;and there are 75self-dual doubly-even binary codes with type of 7-(8,0)when the dimension of E1(σ)*is 4.We discuss the similarities of the extremal self-dual doubly-even binary codes with length of 56 to 70,and obtain the generator matrix and classification.So the generator matrices and classification of the extremal self-dual doubly-even binary codes with length between 50 and 70can be solved completely.更多还原