Artículos de revistas
Algebraic Constructions Of Densest Lattices
Registro en:
Journal Of Algebra. Academic Press Inc., v. 429, n. , p. 218 - 235, 2015.
218693
10.1016/j.jalgebra.2014.12.044
2-s2.0-84922989466
Autor
Jorge G.C.
Andrade A.A.D.
Costa S.I.R.
Strapasson J.E.
Institución
Resumen
The aim of this paper is to investigate rotated versions of the densest known lattices in dimensions 2, 3, 4, 5, 6, 7, 8, 12 and 24 constructed via ideals and free Z-modules that are not ideals in subfields of cyclotomic fields. The focus is on totally real number fields and the associated full diversity lattices which may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. We also discuss on the existence of a number field K such that it is possible to obtain the lattices A2, E6 and E7 via a twisted embedding applied to a fractional ideal of OK. 429
218 235 Andrade, A.A., Carvalho, E.D., Construction of ideal lattices with full diversity (2011) J. Adv. Res. Appl. Math., 3 (3), pp. 82-92 Andrade, A.A., Ferrari, A.J., Benedito, C.W.O., Costa, S.I.R., Constructions of algebraic lattices (2010) Comput. Appl. Math., 29 (3), pp. 493-505 Bayer-Fluckiger, E., Lattices and number fields (1999) Contemp. Math., 241, pp. 69-84 Bayer-Fluckiger, E., Ideal lattices (2002) Proceedings of the Conference Number Theory and Diophantine Geometry, pp. 168-184. , Cambridge Univ. Press Bayer-Fluckiger, E., Determinants of integral ideal lattices and automorphisms of given characteristic polynomial (2002) J. Algebra, 257, pp. 215-221 Bayer-Fluckiger, E., Oggier, F., Viterbo, E., New algebraic constructions of rotated Zn-lattice constellations for the Rayleigh fading channel (2004) IEEE Trans. Inform. Theory, 50 (4), pp. 702-714 Bayer-Fluckiger, E., Nebe, G., On the Euclidean minimum of some real number fields (2005) J. Théor. Nombres Bordeaux, 17 (2), pp. 437-454 Bayer-Fluckiger, E., Suarez, I., Ideal lattices over totally real number fields and Euclidean minima (2006) Arch. Math., 86 (3), pp. 217-225 Boutros, J., Viterbo, E., Rastello, C., Belfiori, J.C., Good lattice constellations for both Rayleigh fading and Gaussian channels (1996) IEEE Trans. Inform. Theory, 42 (2), pp. 502-517 Craig, M., Extreme forms and cyclotomy (1978) Mathematika, 25, pp. 44-56 Craig, M., A cyclotomic construction of the Leech's lattice (1978) Mathematika, 25, pp. 236-241 Conway, J.H., Sloane, N.J.A., (1998) Sphere Packings, Lattices and Groups, , Springer-Verlag Cohn, H., Kumar, A., Optimality and uniqueness of the Leech lattice among lattices (2009) Ann. of Math., 170, pp. 1003-1050. , Princeton Fincke, U., Pohst, M., Improved methods for calculating vectors of short length in a lattice, including a complexity analysis (1985) Math. Comp., 44 (170), pp. 463-471. , AMS Flores, A.L., Interlando, J.C., Nóbrega Neto, T.P., Contiero, A.L., A new number field construction of the lattice E8 (2012) Contrib. Algebra Geom., 56, pp. 1-6. , Springer Haviv, I., Regev, O., On the lattice isomorphism problem, , arxiv:1311.0366 Jorge, G.C., Ferrari, A.J., Costa, S.I.R., Rotated Dn-lattices (2012) J. Number Theory, 132, pp. 2397-2406 Jorge, G.C., Costa, S.I.R., On rotated Dn-lattices constructed via totally real number fields (2013) Arch. Math., 100, pp. 323-332 Oggier, F., Viterbo, E., Algebraic number theory and code design for Rayleigh fading channels (2004) Found. Trends Commun. Inf. Theory, 1 (3), pp. 333-415 Oggier, F., (2005) Algebraic methods for channel coding, , Ph.D. Thesis, École Polytechnique Fédérale de Laussane, Laussane Oggier, F., Bayer-Fluckiger, E., Best rotated cubic lattice constellations for the Rayleigh fading channel (2013) Proceedings of IEEE International Symposium on Information Theory Samuel, P., (1970) Algebraic Theory of Numbers, , Hermann, Paris Stewart, I.N., Tall, D.O., (1987) Algebraic Number Theory, , Chapman & Hall, London Viterbo, E., Boutros, J., A universal lattice code decoder for fading channels (1999) IEEE Trans. Inform. Theory, 45 (5), pp. 1639-1642