Codes in algebras of direct products of groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909963252662272 |
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| author | Sales-Cabrera, Miguel Soler-Escrivà, Xaro Sotomayor, Víctor |
| author_facet | Sales-Cabrera, Miguel Soler-Escrivà, Xaro Sotomayor, Víctor |
| contents | In this paper we obtain the Wedderburn-Artin decomposition of a semisimple group algebra associated to a direct product of finite groups. We also provide formulae for the number of all possible group codes, and their dimensions, that can be constructed in a group algebra. As particular cases, we present the complete algebraic description of the group algebra of any direct product of groups whose direct factors are cyclic, dihedral, or generalised quaternion groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_09695 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Codes in algebras of direct products of groups Sales-Cabrera, Miguel Soler-Escrivà, Xaro Sotomayor, Víctor Information Theory Quantum Algebra Rings and Algebras 94B05, 16S34, 16D25 In this paper we obtain the Wedderburn-Artin decomposition of a semisimple group algebra associated to a direct product of finite groups. We also provide formulae for the number of all possible group codes, and their dimensions, that can be constructed in a group algebra. As particular cases, we present the complete algebraic description of the group algebra of any direct product of groups whose direct factors are cyclic, dihedral, or generalised quaternion groups. |
| title | Codes in algebras of direct products of groups |
| topic | Information Theory Quantum Algebra Rings and Algebras 94B05, 16S34, 16D25 |
| url | https://arxiv.org/abs/2412.09695 |