Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps

Authors:
Christine Bachoc;Frank Vallentin
Affiliations:
Laboratoire A2X, Université Bordeaux I, 351, cours de la Libération, 33405 Talence, France;Centrum voor Wiskunde en Informatica (CWI), Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
Venue:
European Journal of Combinatorics
Year:
2009

Citing 3
Cited 2

Sphere-packings, lattices, and groups

Sphere-packings, lattices, and groups
Optimal Arrangements in Packing Congruent Balls in a Spherical Container

Discrete & Computational Geometry
Linear programming bounds for codes in grassmannian spaces

IEEE Transactions on Information Theory

Note: Optimality and uniqueness of the (4,10,1/6) spherical code

Journal of Combinatorial Theory Series A
A survey on spherical designs and algebraic combinatorics on spheres

European Journal of Combinatorics

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Abstract

In this paper, we apply the semidefinite programming approach developed in [C. Bachoc, F. Vallentin, New upper bounds for kissing numbers from semidefinite programming, J. Amer. Math. Soc. 21 (2008) 909-924] to obtain new upper bounds for codes in spherical caps. We compute new upper bounds for the one-sided kissing number in several dimensions where, in particular, we get a new tight bound in dimension 8. Furthermore, we show how to use the SDP framework to get analytic bounds.