Commutative group codes in R-4, R-6, R-8 and R-16-Approaching the bound

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Spherical codes in even dimensions n = 2m generated by a commutative group of orthogonal matrices can be determined by a quotient of m-dimensional lattices when the sublattice has an orthogonal basis. We discuss here the existence of orthogonal sublattices of the lattices A(2), D-3, D-4 and E-8, which have the best packing density in their dimensions, in order to generate families of commutative group codes approaching the bound presented in Siqueira and Costa (2008) [14]. (C) 2013 Elsevier B.V. All rights reserved.3131616771687Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [2007/56052-8, 2004/12370-8]CNPq [309561/2009-4