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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

New upper bounds for kissing numbers from semidefinite programming


Authors: Christine Bachoc and Frank Vallentin
Journal: J. Amer. Math. Soc. 21 (2008), 909-924
MSC (2000): Primary 52C17, 90C22
Published electronically: November 29, 2007
MathSciNet review: 2393433
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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$.


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Additional Information

Christine Bachoc
Affiliation: Laboratoire A2X, Université Bordeaux I, 351, cours de la Libération, 33405 Talence, France
Email: bachoc@math.u-bordeaux1.fr

Frank Vallentin
Affiliation: Centrum voor Wiskunde en Informatica (CWI), Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
Email: f.vallentin@cwi.nl

DOI: http://dx.doi.org/10.1090/S0894-0347-07-00589-9
PII: S 0894-0347(07)00589-9
Keywords: Spherical codes, kissing number, semidefinite programming, orthogonal polynomials
Received by editor(s): October 17, 2006
Published electronically: November 29, 2007
Additional Notes: The second author was supported by the Netherlands Organization for Scientific Research under grant NWO 639.032.203 and by the Deutsche Forschungsgemeinschaft (DFG) under grant SCHU 1503/4-1.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.