Twisted skew $G$-codes

TL;DR

This paper explores the structure of left ideals in twisted skew group rings over finite fields, unifying various classes of group codes and providing a framework for understanding their algebraic properties.

Contribution

It introduces a unified approach to group, twisted group, and skew group codes through the study of left ideals in twisted skew group rings.

Findings

Identifies conditions under which these rings produce known codes

Provides a unifying algebraic framework for different code classes

Enhances understanding of code structure via algebraic ideals

Abstract

In this paper we investigate left ideals as codes in twisted skew group rings. The considered rings, which are often algebras over a finite field, allows us to detect many of the well-known codes. The presentation, given here, unifies the concept of group codes, twisted group codes and skew group codes.