Two new classes of projective two-weight linear codes

TL;DR

This paper constructs new classes of projective two-weight linear codes over finite fields, determines their weight distributions, and explores their applications in secret sharing and graph theory.

Contribution

It introduces two novel classes of projective two-weight codes and links them to strongly regular graphs, expanding the understanding of code and graph structures.

Findings

Constructed new projective two-weight codes

Determined complete weight distributions of these codes

Established connections to strongly regular graphs

Abstract

In this paper, for an odd prime $p$, several classes of two-weight linear codes over the finite field $\mathbb{F}_p$ are constructed from the defining sets, and then their complete weight distributions are determined by employing character sums. These codes can be suitable for applications in secret sharing schemes. Furthermore, two new classes of projective two-weight codes are obtained, and then two new classes of strongly regular graphs are given.