Complete weight enumerators of a class of linear codes

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• 作者：Shudi Yang^a ; ^b ; ^{yangshudi7902@126.com} ; Zheng-An Yao^c ; ^{mcsyao@mail.sysu.edu.cn}
• 关键词：Linear code ; Complete weight enumerator ; Gauss sum
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：340
• 期：4
• 页码：729-739
• 全文大小：432 K
• 卷排序：340

文摘

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 mm and tt be positive integers. For an odd prime pp, let r=pmr=pm and TrTr be the absolute trace function from FrFr to FpFp. In this paper, for b∈Fp∗, we define Db=(x1,…,xt)∈Frt:Tr(x1+⋯+xt)=b, and determine the complete weight enumerator of a class of pp-ary linear codes given by CDb={c(a1,a2,…,at):a1,…,at∈Fr},CDb={c(a1,a2,…,at):a1,…,at∈Fr},where c(a1,a2,…,at)=(Tr(a1x12+⋯+atxt2))(x1,…,xt)∈Db.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).