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

Autor(es)

Strapasson, Joao Eloir ; Ferrari, Agnaldo Jose ; Jorge, Grasiele Cristiane ; Costa, Sueli Irene Rodrigues

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. 20, n. 3, p. 23-pg., 2021-03-01.

Resumo

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)

• Processo FAPESP: 13/25977-7 - Segurança e confiabilidade da informação: teoria e prática
• Beneficiário: Marcelo Firer
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 15/17167-0 - Reticulados algébricos via corpos de números abelianos
• Beneficiário: Grasiele Cristiane Jorge
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 14/14449-2 - Construção de reticulados e aplicações na Teoria da Informação
• Beneficiário: Agnaldo José Ferrari
• Modalidade de apoio: Auxílio à Pesquisa - Regular