Complete weight enumerators of a class of linear codes with four or five weights

TL;DR

This paper constructs a class of linear codes over finite fields with four or five weights, determines their complete weight enumerators using Weil sums, and identifies some nearly optimal codes relative to the Griesmer bound.

Contribution

It extends previous work by explicitly determining the weight enumerators of these codes and identifying nearly optimal codes, enhancing understanding of code weight distributions.

Findings

Constructed four-weight and five-weight linear codes over Fp.

Determined complete weight enumerators using Weil sums.

Identified codes close to the Griesmer bound, some being optimal.

Abstract

In this paper, based on the theory of defining sets, a class of four-weight or five-weight linear codes over Fp is constructed. The complete weight enumerators of the linear codes are determined by means of Weil sums. In some case, there is an almost optimal code with respect to Griesmer bound, which is also an optimal one according to the online code table. This is an extension of the results raised by Zhang et al.(2020).