Codes in algebras of direct products of groups

Miguel Sales-Cabrera; Xaro Soler-Escrivà; Víctor Sotomayor

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arXiv · 2412.09695

Codes in algebras of direct products of groups

Miguel Sales-Cabrera·Xaro Soler-Escrivà·Víctor Sotomayor

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Abstract

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.

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Miguel Sales-Cabrera, Xaro Soler-Escrivà, Víctor Sotomayor. 2025-12-15. Codes in algebras of direct products of groups. https://arxiv.org/abs/2412.09695

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