论文标题
关于线性代码的重量分布的公式，并应用于AMDS代码
A formula on the weight distribution of linear codes with applications to AMDS codes
论文作者
论文摘要
自编码理论开始以来，线性代码的重量分布的确定一直是一个令人着迷的问题。关于特殊情况的重量枚举者的研究已经进行了大量研究，例如自动划分的代码和小单身顿缺陷的代码。我们提出了一组新的线性关系，必须通过重量分布的系数来满足。从这些关系中，我们可以为有趣的情况（例如极端代码，遗产代码，MDS和NMDS代码）得出已知的身份（以一种更简单的方式）。此外，我们能够首次提出AMDS代码的重量分布。我们还讨论了结果与PLESS方程之间的联系。
The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and codes with small Singleton's defect. We propose a new set of linear relations that must be satisfied by the coefficients of the weight distribution. From these relations we are able to derive known identities (in an easier way) for interesting cases, such as extremal codes, Hermitian codes, MDS and NMDS codes. Moreover, we are able to present for the first time the weight distribution of AMDS codes. We also discuss the link between our results and the Pless equations.
