Constacyclic codes with best-known parameters

TL;DR

This paper constructs infinite families of q-ary constacyclic codes with near-optimal parameters, including many with best-known minimum distances, advancing coding theory by providing new codes with desirable properties.

Contribution

The paper introduces new infinite families of constacyclic codes with parameters close to optimal, covering various lengths and achieving high minimum distances.

Findings

Constructed infinite families of codes with minimum distance at least cn/ log_q n

Many codes have optimal or near-optimal parameters

Applicable to various code lengths

Abstract

In this paper, we construct several infinite families of $q$-ary constacyclic codes over a finite field $\mathbb{F}_q$ with length $n$, dimension around $n/2$, and minimum distance at least $cn/\log_q n$ for some positive constant $c$. They contain many constacyclic codes with optimal, or almost-optimal, or best-known parameters. We also consider various forms of the length $n$.