Christine Bachoc, Frank Vallentin
Published 2006-08-16, updated 2007-10-03Version 4
Recently A. Schrijver derived new upper bounds for binary codes using semidefinite programming. In this paper we adapt this approach to codes on the unit sphere and we compute new upper bounds for the kissing number in several dimensions. In particular our computations give the (known) values for the cases n = 3, 4, 8, 24.
Comments: 17 pages, (v4) references updated, accepted in Journal of the American Mathematical Society
Journal: J. Amer. Math. Soc. 21 (2008), 909-924
Kissing number in hyperbolic space
Kissing number in spherical space
Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps
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