A family of projective two-weight linear codes

TL;DR

This paper introduces a new family of q-ary projective two-weight linear codes with excellent parameters, which are used to construct strongly regular graphs and secret sharing schemes with novel properties.

Contribution

It presents a novel family of projective two-weight codes over fields of characteristic two, expanding their applications in graph theory and cryptography.

Findings

Codes have excellent parameters and duals.

Derived strongly regular graphs with new parameters.

Designed secret sharing schemes with interesting access structures.

Abstract

Projective two-weight linear codes are closely related to finite projective spaces and strongly regular graphs. In this paper, a family of $q$-ary projective two-weight linear codes is presented, where $q$ is a power of 2. The parameters of both the codes and their duals are excellent. As applications, the codes are used to derive strongly regular graphs with new parameters and secret sharing schemes with interesting access structures.