New upper bounds for kissing numbers from semidefinite programming

Abstract

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.

17 pages, (v4) references updated, accepted in Journal of the American Mathematical Society

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• Nonexistence of tight spherical design of harmonic index 4
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• Using real algebraic geometry to solve combinatorial problems with symmetries
• Bounds for solid angles of lattices of rank three
• Applications of semidefinite programming to coding theory
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