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

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Author(s):	Strapasson, Joao Eloir ; Ferrari, Agnaldo Jose ; Jorge, Grasiele Cristiane ; Costa, Sueli Irene Rodrigues Total Authors: 4
Document type:	Journal article
Source:	JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. 20, n. 3, p. 23-pg., 2021-03-01.
Abstract
In this paper, we construct some families of rotated unimodular lattices and rotated direct sum of Barnes-Wall lattices BWn for n = 4, 8 and 16 via ideals of the ring of the integers DOUBLE-STRUCK CAPITAL Z[zeta 2rq + zeta 2rq(-1)] for q = 3, 5 and 15. We also construct rotated BW16 and BW32-lattices via DOUBLE-STRUCK CAPITAL Z-submodules of DOUBLE-STRUCK CAPITAL Z[zeta 2r15 + zeta 2r15(-1)]. 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. (AU)

FAPESP's process:	13/25977-7 - Security and reliability of Information: theory and practice
Grantee:	Marcelo Firer
Support Opportunities:	Research Projects - Thematic Grants


FAPESP's process:	15/17167-0 - Algebraic lattices via abelian number fields
Grantee:	Grasiele Cristiane Jorge
Support Opportunities:	Regular Research Grants


FAPESP's process:	14/14449-2 - Construction of lattices and applications in Information Theory
Grantee:	Agnaldo José Ferrari
Support Opportunities:	Regular Research Grants