Several classes of projective few-weight linear codes and their applications

TL;DR

This paper explores classes of projective few-weight linear codes, highlighting their applications in secret sharing, combinatorial designs, and related structures, and introduces new code constructions with potential practical benefits.

Contribution

The paper introduces new classes of projective few-weight linear codes and demonstrates their applications in secret sharing schemes and combinatorial structures.

Findings

New classes of projective few-weight linear codes

Codes with applications in secret sharing schemes

Connections to finite projective spaces and combinatorial designs

Abstract

It is well-known that few-weight linear codes have better applications in secret sharing schemes \cite{JY2006,CC2005}.In particular, projective two-weight codes are very precious as they are closely related to finite projective spaces, strongly regular graphs and combinatorial designs \cite{RC1986,CD2018,P1972}. Here, we present the following two applications.