Two matrix-based lattice construction techniques
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Data
2013-04-01
Autores
Carmelo Interlando, J.
Da Nóbrega Neto, Trajano Pires [UNESP]
Flores, André Luiz
Dantas Lopes, José Othon
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Resumo
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.
Descrição
Palavras-chave
Generator matrices, Geometry of numbers, Lattices, Sphere packings, Generator matrix, Lattice construction, Sub-lattices, Crystal lattices, Number theory, Packing
Como citar
Linear Algebra and Its Applications, v. 438, n. 7, p. 3001-3010, 2013.