一类基于特征函数构造的极小线性码

Minimal linear codes from a class of characteristic functions

具有较低重量的线性码在通信、数据存储和信息安全等领域均有重要作用,因此低重线性码的构造一直是编码理论的重要研究方向.利用特征函数构造极小码的方法,通过选取适当的定义集,构造了一类具有较低重量的极小线性码,该线性码是不满足Ashikhmin-Barg条件的极小码,可用于设计具有良好访问结构的秘密共享方案.

Linear codes with a few weights play an important role in communication,data storage and information security.Therefore,the construction of linear codes with a few weights is a very important research area of coding theory.Based on the theory of constructing minimal codes of characteristic functions,by selecting definition sets properly,a class of minimal linear codes with a few weights are constructed.The linear codes obtained in this paper are minimal codes that do not satisfy the Ashikhmin-Barg condition,and it can be used to design a secret sharing scheme with good access structure.