On Codes from Split Metacyclic Groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912331171102720 |
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| author | Vedenev, Kirill |
| author_facet | Vedenev, Kirill |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Codes from Split Metacyclic Groups Vedenev, Kirill Information Theory Rings and Algebras 16S34 (Primary), 94B05 (Secondary) 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. |
| title | On Codes from Split Metacyclic Groups |
| topic | Information Theory Rings and Algebras 16S34 (Primary), 94B05 (Secondary) |
| url | https://arxiv.org/abs/2504.11960 |