Exponent of Cyclic Codes over $\mathbb{F}_q$

TL;DR

This paper introduces the concept of the exponent of cyclic codes over finite fields, explores its relation to dual codes, and determines the exponent distribution, providing new insights into their algebraic structure.

Contribution

It defines the exponent of cyclic codes, establishes its relation to dual codes, and characterizes the exponent distribution, advancing understanding of cyclic code properties.

Findings

Defined the exponent of cyclic codes over finite fields

Established the relation between the exponent of a code and its dual

Determined the exponent distribution of cyclic codes

Abstract

In this article, we introduce and study the concept of the exponent of a cyclic code over a finite field $\mathbb{F}_q.$ We give a relation between the exponent of a cyclic code and its dual code. Finally, we introduce and determine the exponent distribution of the cyclic code.