Complete weight enumerators of a class of linear codes

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 b∈Fp∗, we define Db=(x1,…,xt)∈Frt:Tr(x1+⋯+xt)=b, and determine the complete weight enumerator of a class of p-ary linear codes given by 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).