Commutative group codes in R4, R6, R8 and R16-Approaching the bound - Alves, Carina [UNESP]; Costa, Sueli I. R. (Elsevier, 2013)
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 A2, D3, D4 and E8, 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]. © 2013 Elsevier B.V. All rights reserved.
Keywords: Group codes; Lattices; Minimum distance; Packing density; Spherical codes