环F_(q)+vF_(q)上线性码的重量计数器

The Weight Enumerators of Linear Codes over the Ring F_(q)+vF_(q)

设F_(q)为_(q)元有限域,R=F_(q)+vF_(q)(v^(2)=v).首先,研究R上线性码的基本性质;其次,通过定义Lee重量引入长度重量计数器,得到Lee重量计数器、Hamming重量计数器、对称重量计数器及长度重量计数器的关系;最后,给出长度重量计数器关于线性码直和分解的代数性质.

Let F_(q) be a finite field with q elements,and R=F_(q)+vF_(q)(v^(2)=v).In this article,we study the basic properties of linear codes over R.Then,by defining the Lee weight,we introduce the length weight enumerator and obtain the relationship among the Lee weight enumerator,the Hamming weight enumerator,the symmetrized weight enumerator and the length weight enumerator.Finally,give the algebraic properties of the length weight enumerator on direct sum decompositions of linear codes.