A Class of Two-Weight and Three-Weight Linear Codes and Their Duals

TL;DR

This paper constructs and analyzes a new class of linear codes with two and three nonzero weights using trace functions, determining their weight distributions and exploring their duals for potential cryptographic applications.

Contribution

It introduces a novel class of linear codes with specified weight distributions and studies their duals, demonstrating optimality and potential use in cryptography.

Findings

Codes include some optimal codes meeting bounds

Dual codes are proven to be optimal or nearly optimal

Codes have applications in cryptography and combinatorics

Abstract

The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some optimal codes, which meets certain bound on linear codes. The dual codes are also studied and proved to be optimal or almost optimal. These codes may have applications in authentication codes, secret sharing schemes and strongly regular graphs.