Several classes of three-weight or four-weight linear codes

TL;DR

This paper constructs new classes of three-weight and four-weight linear codes over F2 using defining sets, determines their weight distributions, and explores their applications in secret sharing schemes.

Contribution

It introduces novel constructions of projective three-weight and four-weight linear codes over F2 with explicit weight distributions and potential cryptographic applications.

Findings

Constructed a class of projective three-weight linear codes.

Developed two classes of projective four-weight linear codes.

Identified applications in secret sharing schemes.

Abstract

In this manuscript, we construct a class of projective three-weight linear codes and two classes of projective four-weight linear codes over F2 from the defining sets construction, and determine their weight distributions by using additive characters. Especially, the projective three-weight linear code and one class of projective four-weight linear codes (Theorem 4.1) can be applied in secret sharing schemes.