Constructions of algebraic lattices

In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2,3,4,6,8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via ideals of a ring of algebraic integers. Mathematical subject classification: 18B35, 94A15, 20H10.

On the Optimality of Finite Constellations from Algebraic Lattices

A construction technique of finite point constellations in n-dimensional spaces from ideals in rings of algebraic integers is described. An algorithm is presented to find constellations with minimum average energy from a given lattice. For comparison, a numerical table of lattice constellations and group codes is computed for spaces of dimension two, three, and four. © 2001.

Constructions of ideal lattices with full diversity

In this paper, we present new constructions of ideal lattices for the Rayleigh fading channel in Euclidean spaces with full diversity. These constructions are through totally real subfields of cyclotomic fields, obtained by endowing their ring of integers. With this method we reproduce rotated versions of algebraic lattices where the performance in terms of minimum product distance is related with the field determinant.

Lattices from subfields of Q (xi n)

In this paper we present a method for evaluating the center density of algebraic lattices from subfields of Q(xi n), where n is a positive integer. This method allows to reproduce rotated versions of dense lattices in some dimensions. Constellations on algebraic lattices with high packing density have been proposed for use in communications in Gaussian channels and also in Rayleigh fading channels in case they have high diversity.

Construções de reticulados via extensões cíclicas de grau ímpar

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Corpos abelianos com aplicações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Reticulados algébricos via corpos abelianos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Famílias de reticulados algébricos e reticulados ideais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Discriminante de corpos de números

Pós-graduação em Matemática - IBILCE

Anéis de inteiros de corpos de números e aplicações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma contribuição a teoria dos números e reticulados

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Algebraic constructions of densest lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Lattices from maximal orders into quaternion algebras

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

GLOBAL DYNAMICS of THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stretched-exponential behavior and random walks on diluted hypercubic lattices

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)