Two classes of constacyclic codes with a square-root-like lower bound

TL;DR

This paper constructs and analyzes infinite classes of constacyclic and negacyclic codes over finite fields, including self-dual codes with a square-root-like minimum distance bound, advancing coding theory with new code families.

Contribution

It introduces new infinite classes of negacyclic and constacyclic codes with specific lengths and properties, including self-dual codes with improved minimum distance bounds.

Findings

Constructed infinite classes of negacyclic codes of length (q^m-1)/2

Developed infinite classes of constacyclic codes of length (q^m-1)/(q-1)

Presented ternary negacyclic self-dual codes with square-root-like minimum distance

Abstract

Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic structure. In this paper, an infinite class of $q$-ary negacyclic codes of length $(q^m-1)/2$ and an infinite class of $q$-ary constacyclic codes of length $(q^m-1)/(q-1)$ are constructed and analyzed. As a by-product, two infinite classes of ternary negacyclic self-dual codes with a square-root-like lower bound on their minimum distances are presented.