On Codes from Split Metacyclic Groups
Abstract
The paper presents a comprehensive study of group codes from non-abelian split metacyclic group algebras. We derive an explicit Wedderburn-like decomposition of finite split metacyclic group algebras over fields with characteristic coprime to the group order. Utilizing this decomposition, we develop a systematic theory of metacyclic codes, providing their algebraic description and proving that they can be viewed as generalized concatenated codes with cyclic inner codes and skew quasi-cyclic outer codes. We establish bounds on the minimum distance of metacyclic codes and investigate the class of induced codes. Furthermore, we show the feasibility of constructing a partial key-recovery attack against certain McEliece-type cryptosystems based on metacyclic codes by exploiting their generalized concatenated structure.
Keywords
Cite
@article{arxiv.2504.11960,
title = {On Codes from Split Metacyclic Groups},
author = {Kirill Vedenev},
journal= {arXiv preprint arXiv:2504.11960},
year = {2025}
}