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Please use this identifier to cite or link to this item: http://acervodigital.unesp.br/handle/11449/22155
Title: 
An Extension of Craig's Family of Lattices
Author(s): 
Institution: 
  • Universidade Federal de Alagoas (UFAL)
  • San Diego State Univ
  • Universidade Estadual Paulista (UNESP)
ISSN: 
0008-4395
Abstract: 
Let p be a prime, and let zeta(p) be a primitive p-th root of unity. The lattices in Craig's family are (p - 1)-dimensional and are geometrical representations of the integral Z[zeta(p)]-ideals < 1 - zeta(p)>(i), where i is a positive integer. This lattice construction technique is a powerful one. Indeed, in dimensions p - 1 where 149 <= p <= 3001, Craig's lattices are the densest packings known. Motivated by this, we construct (p - 1)(q - 1)-dimensional lattices from the integral Z[zeta(pq)]-ideals < 1 - zeta(p)>(i) < 1 - zeta(q)>(j), where p and q are distinct primes and i and fare positive integers. In terms of sphere-packing density, the new lattices and those in Craig's family have the same asymptotic behavior. In conclusion, Craig's family is greatly extended while preserving its sphere-packing properties.
Issue Date: 
1-Dec-2011
Citation: 
Canadian Mathematical Bulletin-bulletin Canadien de Mathematiques. Ottawa: Canadian Mathematical Soc, v. 54, n. 4, p. 645-653, 2011.
Time Duration: 
645-653
Publisher: 
Canadian Mathematical Soc
Keywords: 
  • geometry of numbers
  • lattice packing
  • Craig's lattices
  • Quadratic form
  • Cyclotomic fields
Source: 
http://dx.doi.org/10.4153/CMB-2011-038-7
URI: 
Access Rights: 
Acesso restrito
Type: 
outro
Source:
http://repositorio.unesp.br/handle/11449/22155
Appears in Collections:Artigos, TCCs, Teses e Dissertações da Unesp

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