几类二重和三重线性码的构造

A construction of several classes of two-weight and three-weight linear codes

较低重量的线性码可应用于秘密共享方案、鉴别代码、结合方案等领域.利用定义集构造线性码是编码理论的一个重要研究方向,如果定义集选择恰当,可以得到一些较低重量的线性码.文中利用由定义集设计线性码的方法,构造了几类二重和三重的线性码,基于特征和理论得到了该码重量分布的精确值.研究表明,所设计的线性码均为二重或者三重的,并且可应用于秘密共享方案.

Linear codes with a few weights can be applied in secret sharing schemes,authentication codes and association schemes.Constructing linear codes from defining sets is an important research direction in coding theory.If the defining sets are well chosen,a few nonzero-weight linear codes can be obtained.In this paper,several classes of two-weight and three-weight linear codes are constructed from a new defining set and their explicit weight distribution are obtained using exponential sums.Researches show that these codes are all two-weight or three-weight and may have applications in secret sharing scheme.