Constacyclic Codes over Finite Fields

TL;DR

This paper introduces an isometry-based classification for constacyclic codes over finite fields and characterizes their polynomial generators for specific lengths involving prime powers.

Contribution

It presents a new isometry relation for classifying constacyclic codes and characterizes their generators for lengths of the form ^t p^s, expanding understanding of their structure.

Findings

Introduces a novel isometry relation for classifying constacyclic codes.

Provides explicit characterization of polynomial generators for certain code lengths.

Enhances the structural understanding of constacyclic codes over finite fields.

Abstract

An equivalence relation called isometry is introduced to classify constacyclic codes over a finite field; the polynomial generators of constacyclic codes of length $\ell^tp^s$ are characterized, where $p$ is the characteristic of the finite field and $\ell$ is a prime different from $p$.