Constructions of algebraic lattices
In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2,3,4,6,8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via...
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| Published in | Computational & applied mathematics Vol. 29; no. 3; pp. 493 - 505 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Sociedade Brasileira de Matemática Aplicada e Computacional
2010
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1807-0302 |
| DOI | 10.1590/S1807-03022010000300010 |
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| Abstract | In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2,3,4,6,8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via ideals of a ring of algebraic integers. Mathematical subject classification: 18B35, 94A15, 20H10. |
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| AbstractList | In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2,3,4,6,8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via ideals of a ring of algebraic integers. Mathematical subject classification: 18B35, 94A15, 20H10. |
| Author | Costa, S.I.R Ferrari, A.J Benedito, C.W.O Andrade, A.A |
| AuthorAffiliation | Universidade Estadual Paulista Universidade Estadual de Campinas |
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| Keywords | algebraic number field twisted canonical homomorphism center density algebraic lattice |
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| References | Bayer-Fluckiger, E. 1999 Giraud, X.; Belfiore, J.C. 1996; 42-1 Samuel, P. 1970 Bayer-Fluckiger, E. 2006; 86 Boutros, J.; Viterbo, E.; Rastello, C.; Belfiore, J-C. 1996; 42-2 Bayer-Fluckiger, E. 1999; 241 Bayer-Fluckiger, E.; Martinet, J. 1994; 451 Bayer-Fluckiger, E. 2000; 12 Bayer-Fluckiger, E. 2005; 114 Conway, J.H.; Sloane, N.J.A. 1999 Bayer-Fluckiger, E. 1984; 59 Souza, T.M. 2004 |
| References_xml | – volume: 12 start-page: 273 year: 2000 end-page: 280 article-title: Cyclotomic modular lattices publication-title: Journal de Théorie des Nombres de Bordeaux – volume: 42-2 start-page: 502 year: 1996 end-page: 517 article-title: Good lattice constellations for both Rayleigh fading and Gaussian channels publication-title: IEEE Trans. Inform. Theory – volume: 451 start-page: 51 year: 1994 end-page: 69 article-title: Formes quadratiques liées aux algèbres semi-simples publication-title: J. Reine Angew. Math. – volume: 86 start-page: 217 year: 2006 end-page: 225 article-title: Ideal lattices over totally real number fields and euclidian minima publication-title: Archiv Math. – volume: 241 start-page: 69 year: 1999 end-page: 84 article-title: Lattices and number fields publication-title: Contemporany Mathematics – volume: 114 start-page: 394 year: 2005 end-page: 411 article-title: Modular lattices over cyclotomic fields publication-title: Journal of Number Theory – volume: 42-1 start-page: 106 year: 1996 end-page: 115 article-title: Constellations matched to the Rayleigh fading channel publication-title: IEEE Trans. on Inform. Theory – year: 1999 publication-title: Sphere packing, lattices and groups – year: 2004 publication-title: Algebraic lattices in Abelian number field – volume: 59 start-page: 509 year: 1984 end-page: 538 article-title: Definite unimodular lattices having an automorphism of given characteristic polynomial publication-title: Comment. Math. Helvetici – start-page: 168 year: 1999 end-page: 184 publication-title: Ideal lattices – year: 1970 publication-title: Algebraic theory of numbers |
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| Title | Constructions of algebraic lattices |
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