Linear Codes from a Generic Construction

TL;DR

This paper explores a generic method for constructing linear codes over finite fields, establishing relationships among different classes, deriving new codes with improved parameters, and presenting applications in secret sharing.

Contribution

It introduces a unified framework linking various linear code classes, enabling the derivation of new codes and their parameters from existing ones, and presents a new class of three-weight binary codes.

Findings

Relationships among classes of linear codes established

New codes with improved parameters derived

Applications in secret sharing demonstrated

Abstract

A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach. The first objective of this paper is to establish relationships among some classes of linear codes obtained with this approach, so that the parameters of some classes of linear codes can be derived from those of other classes with known parameters. In this way, linear codes with new parameters will be derived. The second is to present a class of three-weight binary codes and consider their applications in secret sharing.