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Applicable Algebra in Engineering, Communication and Computing

08-07-2024 | Original Paper

Algebraic lattices coming from \({\mathbb {Z}}\)-modules generalizing ramified prime ideals in odd prime degree cyclic number fields

Authors: Antonio Aparecido de Andrade, Robson Ricardo de Araujo, Trajano Pires da Nobrega Neto, Jefferson Luiz Rocha Bastos

Published in: Applicable Algebra in Engineering, Communication and Computing

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Abstract

Lattice theory has shown to be useful in information theory, and rotated lattices with high modulation diversity have been extensively studied as an alternative approach for transmission over a Rayleigh fading channel, where the performance depends on the minimum product distance to achieve coding gains. The maximum diversity of a rotated lattice is guaranteed when we use totally real number fields and the minimum product distance is optimized by considering fields with minimum discriminants. With the construction of full-diversity algebraic lattices as our goal, in this work we present and study constructions of full-diversity algebraic lattices in odd prime dimensional Euclidean spaces from families of modules in cyclic number fields. These families include all the ramified prime ideals in each of these number fields. As immediate applications of our results, we present algebraic constructions from the densest lattices in dimensions 3 and 5.

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Title: Algebraic lattices coming from -modules generalizing ramified prime ideals in odd prime degree cyclic number fields
Authors: Antonio Aparecido de Andrade
Robson Ricardo de Araujo
Trajano Pires da Nobrega Neto
Jefferson Luiz Rocha Bastos
Publication date: 08-07-2024
Publisher: Springer Berlin Heidelberg
Published in: Applicable Algebra in Engineering, Communication and Computing
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-024-00666-2

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