Complete Weight Enumerators of a Family of Three-Weight Linear Codes

Abstract: Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime $p$, we present the explicit complete weight enumerator of a family of $p$-ary linear codes constructed with defining set. The weight enumerator is an mmediate result of the complete weight enumerator, which shows that the codes proposed in this paper are three-weight linear codes. Additionally, all nonzero codewords are minimal and thus they are suitable for secret sharing.