论文标题
在两个重量代码上
On two-weight codes
论文作者
论文摘要
我们考虑$ Q $ - ARY（线性和非线性）块代码，具有两个距离：$ d $和$ d+δ$。给出了最佳代码的几种组合结构。在线性（但不是必需的投影）情况下，我们证明在某些条件下，具有$δ> 1 $的线性$ 2 $加权代码的存在意味着以下伟大的公共除数的平等：$（d，q）=（δ，q）$。此类代码的最大基数的上限是通过线性编程和少数距离球形代码得出的。出现了小$ q = 2,3,4 $和$ q \，n <50 $的下限和上限的表。
We consider $q$-ary (linear and nonlinear) block codes with exactly two distances: $d$ and $d+δ$. Several combinatorial constructions of optimal such codes are given. In the linear (but not necessary projective) case, we prove that under certain conditions the existence of such linear $2$-weight code with $δ> 1$ implies the following equality of great common divisors: $(d,q) = (δ,q)$. Upper bounds for the maximum cardinality of such codes are derived by linear programming and from few-distance spherical codes. Tables of lower and upper bounds for small $q = 2,3,4$ and $q\,n < 50$ are presented.
