A class of two or three weights linear codes and their complete weight enumerators

TL;DR

This paper investigates a class of two- or three-weight linear codes using quadratic forms and Weil sums, providing their weight enumerators and identifying some optimal punctured codes.

Contribution

It generalizes previous results by determining complete weight enumerators for these codes using advanced algebraic techniques.

Findings

Derived explicit weight enumerators for the codes.

Identified punctured codes that are optimal or near-optimal.

Extended previous classifications of linear codes with few weights.

Abstract

In the past few years, linear codes with few weights and their weight analysis have been widely studied. In this paper, we further investigate a class of two-weight or three-weight linear codes from defining sets and determine their weight and complete weight enumerators by application of the theory of quadratic forms and some special Weil sums over finite fields. Some punctured codes of the discussed linear codes are optimal or almost optimal with respect to the Griesmer bound. This paper generalizes some results in \cite{ZhuXu2017,Jian2019}.