A Class of Three-Weight Linear Codes and Their Complete Weight Enumerators

TL;DR

This paper introduces a new class of three-weight linear codes over finite fields, explicitly determining their weight enumerators, and demonstrating their potential applications in authentication and secret sharing schemes.

Contribution

The paper proposes a novel class of p-ary linear codes with three weights, providing explicit formulas for their weight enumerators and exploring their practical applications.

Findings

Codes have exactly three weights.

Explicit formulas for weight enumerators are derived.

Suitable for authentication and secret sharing schemes.

Abstract

Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. In this paper, for an odd prime $p$, we propose a class of $p$-ary linear codes by choosing a proper defining set. Their weight enumerators and complete weight enumerators are presented explicitly. The results show that they are linear codes with three weights and suitable for the constructions of authentication codes and secret sharing schemes.