Binary linear codes with at most 4 weights

TL;DR

This paper constructs a new class of binary linear codes with at most four weights, analyzes their weight distribution, and explores their application in secret sharing schemes.

Contribution

It introduces a novel class of binary linear codes with limited weights and determines their weight distribution, expanding their potential applications.

Findings

Codes are at most 4-weight linear codes

Weight distribution is explicitly determined

Codes are applicable in secret sharing schemes

Abstract

For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight distribution is determined. Results show that they are at most 4-weight linear codes. Additionally, these codes can be used in secret sharing schemes.