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.
翻译：线性代码重量分布的确定自编码理论开始以来就是一个令人着迷的问题。对特殊案例的重量计算员进行了大量研究,例如自成一体的代码和单质小的缺陷的代码。我们提出了一套新的线性关系,必须用重量分布系数来满足。从这些关系中,我们可以(以较容易的方式)为一些有趣的案例获得已知身份,如极端代码、埃米提亚代码、MDS和NDDS代码。此外,我们第一次能够展示AMDS代码的重量分布。我们还讨论了我们的结果与Pless方程式之间的联系。
相关内容
微信扫码咨询专知VIP会员