环F_2+vF_2+v^2F_2上线性码的深度分布

The depth distribution of linear codes over F_2+vF_2+v^2F_2

主要研究环R=F_2+vF_2+v^2F_2上线性码的深度分布及其深度谱,其中v3=v.基于在环R上的线性码与它们的生成矩阵研究,可以获得在有限域F2上的线性码C_1,C_v,C_v2与它们的生成矩阵.利用线性码C_1,C_v,C_v2之间的关系,得到了环R上线性码的深度分布及其深度谱.

In this paper, we study the depth distribution and the depth spectrum of linear codes over the ring R =F2＋vF2＋v^2F2,where v^3 = v. Based on the linear codes over R and their generator matrices, the linear codes C1 , Cv , Cv^2 over F2 and their generator matrices are obtained. By using the relationship of C1 , Cv , Cv^2 , the depth distribution and the depth spectrum of linear codes over R are obtained.