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

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

2006-10-27

arxiv.org/abs/math/0610856v2

Europ. J. Comb. 30 (2009), 625-637.

Mathematics

Metric Geometry

15 pages, (v2) referee comments and suggestions incorporated

Scientific paper

10.1016/j.ejc.2008.07.017

We apply the semidefinite programming approach developed in
arxiv:math.MG/0608426 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 we in particular get a new tight bound in dimension 8.
Furthermore we show how to use the SDP framework to get analytic bounds.

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