Twisted skew $G$-codes
Angelot Behajaina, Martino Borello, Javier de la Cruz, Wolfgang, Willems

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.
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research · Cooperative Communication and Network Coding
