环R=F_3+vF_3(v^2=1)上线性码的深度谱  

The Depth Spectra of Linear Codes over R=F_3+vF_3(v^2=1)

作　　者：李建[1] 廖群英[1] LI Jian;LIAO Qunying(Institute of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan, 610066, P. R. China)

机构地区：[1]四川师范大学数学与软件科学学院,成都四川610066

出　　处：《数学进展》2018年第4期635-640,共6页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11401408);四川省科技厅科研重点项目(No.2016JY0134)

摘　　要：设q为素数的方幂,F_q为q元有限域.本文通过将F_q上向量的深度概念推广到环R=F_3+vF_3(v^2=1)上,给出R上线性码码字深度的递归算法,进而利用环R上线性码的生成矩阵及环R到F_3的两个加群同态,给出环R上任意长度的线性码深度谱的上下界.并由此推出环R_1=F_P+vF_P(v^2=1)上任意长度的非零线性码深度谱的上下界,其中p为奇质数.Let q be a power of a prime and Fq be the q elements finite field. By generalizing the concept for the depth of vectors from Fq to the ring R = Fa ＋ vFa （v2 = 1）, a recursive algorithm for the depth of the vector over R is obtained. Furthermore, by defining two homo- morphisms from the Abelian group R to F3, the upper bound and lower bound for the depth spectra of linear codes with arbitrary code length over R are obtained based on the generator matrices. And thus the upper bound and lower bound for the depth spectra of linear codes with arbitrary code length over R1 = Fp ＋ vFp （v2 = 1） can be derived, where p is an odd prime.

关 键 词：线性码 深度 深度谱 深度分布 

分 类 号：O157.4[理学—数学]