Galois Self-Dual Constacyclic Codes

TL;DR

This paper introduces Galois inner products and studies Galois self-dual constacyclic codes, providing conditions for their existence and unifying various types of self-dual codes.

Contribution

It generalizes the concept of inner products and offers a uniform method to analyze Galois self-dual constacyclic codes, extending previous results.

Findings

Conditions for existence of Galois self-dual codes

Unified framework for self-dual, iso-dual, and Hermitian self-dual codes

New results on constacyclic code properties

Abstract

Generalizing Euclidean inner product and Hermitian inner product, we introduce Galois inner products, and study the Galois self-dual constacyclic codes in a very general setting by a uniform method. The conditions for existence of Galois self-dual and isometrically Galois self-dual constacyclic codes are obtained. As consequences, the results on self-dual, iso-dual and Hermitian self-dual constacyclic codes are derived.