Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Upper bounds on the minimum distance of spherical codes
IEEE Transactions on Information Theory
Curves on a sphere, shift-map dynamics, and error control for continuous alphabet sources
IEEE Transactions on Information Theory
Graphs, tessellations, and perfect codes on flat tori
IEEE Transactions on Information Theory
Linear block codes over cyclic groups
IEEE Transactions on Information Theory
Spherical codes on torus layers
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
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We show that commutative group spherical codes in R n , as introduced by D. Slepian, are directly related to flat tori and quotients of lattices. As consequence of this view, we derive new results on the geometry of these codes and an upper bound for their cardinality in terms of minimum distance and the maximum center density of lattices and general spherical packings in the half dimension of the code. This bound is tight in the sense it can be arbitrarily approached in any dimension. Examples of this approach and a comparison of this bound with Union and Rankin bounds for general spherical codes is also presented.