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http://acervodigital.unesp.br/handle/11449/74932- Title:
- Two matrix-based lattice construction techniques
- Universidade Estadual Paulista (UNESP)
- San Diego State University
- Universidade Federal de Alagoas (UFAL)
- Universidade Federal do Ceará (UFC)
- 0024-3795
- 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.
- 1-Apr-2013
- Linear Algebra and Its Applications, v. 438, n. 7, p. 3001-3010, 2013.
- 3001-3010
- Generator matrices
- Geometry of numbers
- Lattices
- Sphere packings
- Generator matrix
- Lattice construction
- Sub-lattices
- Crystal lattices
- Number theory
- Packing
- http://dx.doi.org/10.1016/j.laa.2012.10.031
- Acesso restrito
- outro
- http://repositorio.unesp.br/handle/11449/74932
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