A Note on The Enumeration of Euclidean Self-Dual Skew-Cyclic Codes over Finite Fields

TL;DR

This paper derives enumeration formulas for Euclidean self-dual skew-cyclic codes over finite fields, focusing on cases where the code length and automorphism order are coprime or specific cases when they are not.

Contribution

It provides new enumeration formulas for Euclidean self-dual skew-cyclic codes over finite fields under various conditions.

Findings

Enumeration formulas for (n,|θ|)=1 cases

Partial enumeration results for (n,|θ|)>1 cases

Enhanced understanding of self-dual skew-cyclic codes structure

Abstract

In this paper we give the enumeration formulas for Euclidean self-dual skew-cyclic codes over finite fields when $(n,|\theta|)=1$ and for some cases when $(n,|\theta|)>1,$ where $n$ is the length of the code and $|\theta|$ is the order of automorphism $\theta.$