Another $q$-Polynomial Approach to Cyclic Codes

TL;DR

This paper introduces a new $q$-polynomial method for constructing and analyzing cyclic codes over finite fields, expanding on recent approaches by Ding and Ling.

Contribution

It presents an alternative $q$-polynomial framework for all cyclic codes over $ ext{GF}(q)$, broadening the theoretical tools available.

Findings

Provides a new $q$-polynomial approach applicable to all cyclic codes

Enhances understanding of cyclic code structure through polynomial methods

Potentially simplifies code construction and analysis processes

Abstract

Recently, a $q$-polynomial approach to the construction and analysis of cyclic codes over $\gf(q)$ was given by Ding and Ling. The objective of this paper is to give another $q$-polynomial approach to all cyclic codes over $\gf(q)$.