A Riemann hypothesis analogue for self-dual codes
A Riemann hypothesis analogue for self-dual codes
复制标题
自对偶码的黎曼假设类似物
DOI：
10.1090/dimacs/056/09
复制
发表时间：
1999
影响因子：
5
通讯作者：
I. Duursma
中科院分区：
文献类型：
--
作者：
I. Duursma
我们构造了一个关于自对偶码的Riemann假设模拟。如果假设对于足够大的一类自对偶码是正确的，这将意味着改进了自对偶码最小距离的渐近上界[4]。对于给定的代码，该假设是否成立取决于其权重枚举器。对具有已知重量枚举数的码的验证表明，该假设在许多情况下都成立，特别是对于良好的自对偶码，但对于一般的自对偶码则不成立。良好的自对偶码的重量枚举器满足强线性约束。在这篇文章中，我们展示了在一种特殊情况下，黎曼假设的类比是如何从这种线性约束中推导出来的。一般情况是一个悬而未决的问题。
We formulate a Riemann hypothesis analogue for self-dual codes. If the hypothesis is true for a sufficiently large class of self-dual codes, this would imply an improvement of asymptotic upper bounds for the minimum distance of self-dual codes [4]. Whether the hypothesis holds for a given code depends on its weight enumerator. Verification for codes with a known weight enumerator suggests that the hypothesis holds in many cases, in particular for good self-dual codes, but not for self-dual codes in general. Weight enumerators of good self-dual codes satisfy strong linear constraints. In this paper, we show for a special case how the Riemann hypothesis analogue follows from such linear constraints. The general case is left as an open problem.