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Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/11449/74932
Title: 
Two matrix-based lattice construction techniques
Author(s): 
Institution: 
  • Universidade Estadual Paulista (UNESP)
  • San Diego State University
  • Universidade Federal de Alagoas (UFAL)
  • Universidade Federal do Ceará (UFC)
ISSN: 
0024-3795
Abstract: 
Let m and n be integers greater than 1. Given lattices A and B of dimensions m and n, respectively, a technique for constructing a lattice from them of dimension m+n-1 is introduced. Furthermore, if A and B possess bases satisfying certain conditions, then a second technique yields a lattice of dimension m+n-2. The relevant parameters of the new lattices are given in terms of the respective parameters of A,B, and a lattice C isometric to a sublattice of A and B. Denser sphere packings than previously known ones in dimensions 52, 68, 84, 248, 520, and 4098 are obtained. © 2012 Elsevier Inc. All rights reserved.
Issue Date: 
1-Apr-2013
Citation: 
Linear Algebra and Its Applications, v. 438, n. 7, p. 3001-3010, 2013.
Time Duration: 
3001-3010
Keywords: 
  • Generator matrices
  • Geometry of numbers
  • Lattices
  • Sphere packings
  • Generator matrix
  • Lattice construction
  • Sub-lattices
  • Crystal lattices
  • Number theory
  • Packing
Source: 
http://dx.doi.org/10.1016/j.laa.2012.10.031
URI: 
Access Rights: 
Acesso restrito
Type: 
outro
Source:
http://repositorio.unesp.br/handle/11449/74932
Appears in Collections:Artigos, TCCs, Teses e Dissertações da Unesp

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