Algebraic constructions of rotated unimodular lattices and direct sum of Barnes

Algebraic constructions of rotated unimodular lattices and direct sum of Barnes–Wall lattices

Published:2020-02-06 Issue:03 Volume:20 Page:2150029
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Strapasson João Eloir¹,Ferrari Agnaldo José²,Jorge Grasiele Cristiane³,Costa Sueli Irene Rodrigues⁴

Affiliation:

1. School of Applied Sciences, University of Campinas, Limeira, São Paulo 13484-350, Brazil

2. School of Sciences, São Paulo State University (UNESP), Bauru, São Paulo 17033-360, Brazil

3. Institute of Science and Technology, Federal University of São Paulo, São José dos Campos, São Paulo 12247-014, Brazil

4. Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, São Paulo 13083-859, Brazil

Abstract

In this paper, we construct some families of rotated unimodular lattices and rotated direct sum of Barnes–Wall lattices [Formula: see text] for [Formula: see text] and [Formula: see text] via ideals of the ring of the integers [Formula: see text] for [Formula: see text] and [Formula: see text]. We also construct rotated [Formula: see text] and [Formula: see text]-lattices via [Formula: see text]-submodules of [Formula: see text]. Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. The minimum product distances of such constructions are also presented here.

Funder

Fapesp

CNPq

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498821500298

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