Artículos de revistas
Commutative Group Codes In R4, R6, R8 And R16-approaching The Bound
Registro en:
Discrete Mathematics. , v. 313, n. 16, p. 1677 - 1687, 2013.
0012365X
10.1016/j.disc.2013.04.005
2-s2.0-84884813554
Autor
Alves C.
Costa S.I.R.
Institución
Resumen
Spherical codes in even dimensions n = 2m generated by a commutative group of orthogonal matrices can be determined by a quotient of m-dimensional lattices when the sublattice has an orthogonal basis. We discuss here the existence of orthogonal sublattices of the lattices A2, D3, D4 and E8, which have the best packing density in their dimensions, in order to generate families of commutative group codes approaching the bound presented in Siqueira and Costa (2008) [14]. © 2013 Elsevier B.V. All rights reserved. 313 16 1677 1687 Baez, J., The octonions (2001) Bulletin of the American Mathematical Society, 39 (2), pp. 145-205 Banihashemi, A.H., Blake, I., On the trellis complexity of root lattices and their duals (1999) IEEE Transactions on Information Theory, 45 (6) Berstein, M., Sloane, N.J.A., Wright, P.E., On sublattices of the hexagonal lattice (1997) Discrete Mathematics, 170, pp. 29-39 Biglieri, E., Elia, M., Cyclic-group codes for the Gaussian channel (1976) IEEE Transactions on Information Theory, 22, pp. 624-629 Chapman, R., Double circulant constructions of the Leech lattice (2000) Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 69 (3), pp. 287-297 Cohen, H.C., (1993) A Course in Computational Algebraic Number Theory, , Springer-Verlag, New York Conway, J.H., Sloane, N.J.A., Sphere packings (1999) Lattices and Groups, , Springer-Verlag, New York Costa, S.I.R., Muniz, M., Augustini, E., Palazzo, R., Tessellations and perfect codes on flat tori (2004) IEEE Transactions on Information Theory, 50, pp. 2363-2377 Gantmacher, F.R., (1959) The Theory of Matrices, 1. , Chelsea, New York Ingemarsson, I., Group codes for the Gaussian channel (1989) Lecture Notes in Control and Information Sciences, 128, pp. 73-108. , Springer Verlag Loeliger, H., Signals sets matched to groups (1991) IEEE Transactions on Information Theory, 37, pp. 1675-1682 Micciancio, D., Goldwasser, S., (2002) Complexity of Lattice Problems-A Cryptographic Perspective, , Kluwer Academic Publishers, Norwell, Massachusetts, USA Monteiro, F.A., Kschischang, F.R., Trellis detection for random lattices (2011) Proc. of 8th International Symposium on Wireless Communication Systems, Aachen Siqueira, R.M., Costa, S.I.R., Tori, F., Lattices and bounds for commutative group codes (2008) Designs, Codes and Cryptography, 49, pp. 307-321 Slepian, D., Group codes for the Gaussian channel (1968) Bell System Technical Journal, 47, pp. 575-602 Torezzan, C., Costa, S.I.R., Vaishampayan, V.A., Spherical codes on torus layers (2009) Proceedings of the IEEE International Symposium on Information Theory, pp. 2033-2037. , June-July Torezzan, C., Strapasson, J.E., Costa, S.I.R., Siqueira, R.M., Optimum Commutative Group Codes, , (arXiv:1205. 4067 [cs. IT]) Vaishampayan, V.A., Costa, S.I.R., Curves on a sphere, shift-map dynamics and error control for continuous alphabet sources (2003) IEEE Transactions on Information Theory, 49