Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776955 | Discrete Mathematics | 2017 | 11 Pages |
Abstract
Recently, linear codes constructed from defining sets have been studied extensively. They may have a few weights if the defining set is chosen properly. Let m and t be positive integers. For an odd prime p, let r=pm and Tr be the absolute trace function from Fr to Fp. In this paper, for bâFpâ, we define Db=(x1,â¦,xt)âFrt:Tr(x1+â¯+xt)=b, and determine the complete weight enumerator of a class of p-ary linear codes given by CDb={c(a1,a2,â¦,at):a1,â¦,atâFr},where c(a1,a2,â¦,at)=(Tr(a1x12+â¯+atxt2))(x1,â¦,xt)âDb.Then we get their weight enumerators explicitly, which will give us several linear codes with a few weights. As a generalization of Wang et al. (arXiv:1512.03866), this paper extends the result of Ahn et al. (2016).
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Shudi Yang, Zheng-An Yao,