On the complete weight enumerators of some linear codes with a few weights

TL;DR

This paper determines the complete weight enumerators of certain linear codes with few weights, providing insights into their weight distributions using Legendre symbol sums, which are valuable for various applications.

Contribution

It introduces methods to explicitly compute the complete weight enumerators of specific linear codes with few weights, advancing understanding of their structure.

Findings

Complete weight enumerators derived for selected linear codes.

Hamming weight distributions obtained from these enumerators.

Method involving Legendre symbol sums used for calculations.

Abstract

Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of linear codes are important research topics. In this paper, we consider some classes of linear codes with a few weights and determine the complete weight enumerators from which the corresponding Hamming weight distributions are derived with help of some sums involving Legendre symbol.