两类低重量线性码

Two Classes of Low Weight Linear Codes

线性码具备理想的代数结构,也是纠错码理论的研究焦点之一.特别地,低重量线性码在电子通信行业中有重要作用,例如,通信系统、数据储存系统和消费类电子产品.所以,有必要确定构造出的线性码的重量分布.选定合适的定义集,利用构造线性码的一般方法构造出两类线性码,并通过高斯和理论得到两类线性码的重量分布.

Linear code has ideal algebraic structure and is one of the focus of error-correcting code theory.In particular,low weight linear codes play an important role in the electronic communications industry,such as communications systems,data storage systems,and consumer electronics.Therefore,it is necessary to determine the weight distribution of the constructed linear code.Two kinds of linear codes are constructed by the general method of constructing linear codes,and the weight distribution of the two kinds of linear codes is obtained by Gauss sum theory.