Constructions of linear codes with two or three weights from vectorial dual-bent functions

TL;DR

This paper introduces new constructions of q-ary linear codes with two or three weights derived from vectorial dual-bent functions, providing explicit weight distributions and applications to secret sharing schemes.

Contribution

It presents novel methods to construct q-ary linear codes with few weights from vectorial dual-bent functions, expanding the existing code families and their applications.

Findings

Complete weight distributions of the constructed codes are determined.

Some codes meet the Griesmer bound, indicating optimality.

Constructed codes enable the design of secret sharing schemes with interesting access structures.

Abstract

Linear codes with a few weights are an important class of codes in coding theory and have attracted a lot of attention. In this paper, we present several constructions of $q$-ary linear codes with two or three weights from vectorial dual-bent functions, where $q$ is a power of an odd prime $p$. The weight distributions of the constructed $q$-ary linear codes are completely determined. We illustrate that some known constructions in the literature can be obtained by our constructions. In some special cases, our constructed linear codes can meet the Griesmer bound. Furthermore, based on the constructed $q$-ary linear codes, we obtain secret sharing schemes with interesting access structures.