Flat tori, lattices and bounds for commutative group codes |
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Authors: | Rogério M. Siqueira Sueli I. R. Costa |
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Affiliation: | 1. School of Arts, Science and Humanities, University of S?o Paulo, Sao Paulo, Brazil 2. Institut of Mathematics, State University of Campinas, Sao Paulo, Brazil
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Abstract: | 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. |
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