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On Space-Time Codes Arising from Free Modules and Algebras over an Integral Domain

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Non-Associative and Non-Commutative Algebra and Operator Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 160))

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Abstract

Let R be an integral domain, K its field of fractions, and M n (R) the R-algebra of square matrices of order n and entries from R. In this paper we present two ways of constructing space-time block codes as submodules of M n (R) for n ≥ 1: first, by embedding free associative R-algebras of finite rank n with no zero divisors into M n (R); second, by injecting free R-modules of finite rank n into M n (R) ∩ GL n (K) ∪{ 0}. Some examples of such space-time block codes are given.

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Author information

Authors and Affiliations

  1. Department of Mathematics, King Khalid University, Box 9004, Abha, Saudi Arabia

    Mhammed Boulagouaz & Abdulaziz Deajim

Authors
  1. Mhammed Boulagouaz
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  2. Abdulaziz Deajim
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Corresponding author

Correspondence to Mhammed Boulagouaz .

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Editors and Affiliations

  1. Departement de Mathematiques et Informatique, Faculté des Sciences et Techniques, Université Cheikh Anta Diop, Dakar, Senegal

    Cheikh Thiécoumbe Gueye

  2. Department of Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Málaga, Málaga, Spain

    Mercedes Siles Molina

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Boulagouaz, M., Deajim, A. (2016). On Space-Time Codes Arising from Free Modules and Algebras over an Integral Domain. In: Gueye, C., Molina, M. (eds) Non-Associative and Non-Commutative Algebra and Operator Theory. Springer Proceedings in Mathematics & Statistics, vol 160. Springer, Cham. https://doi.org/10.1007/978-3-319-32902-4_2

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