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Tr. Mat. Inst. Steklova, 2008, Volume 263, Pages 143–158 (Mi tm789)  

This article is cited in 5 scientific papers (total in 5 papers)

Bounds for Codes by Semidefinite Programming

O. R. Musin

Department of Mathematics, University of Texas at Brownsville

Abstract: Delsarte's method and its extensions allow one to consider the upper bound problem for codes in two-point homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that using as variables power sums of distances, this problem can be considered as a finite semidefinite programming problem. This method allows one to improve some linear programming upper bounds. In particular, we obtain new bounds of one-sided kissing numbers.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 263, 134–149

Bibliographic databases:

UDC: 519.14+519.72
Received in August 2008
Language:

Citation: O. R. Musin, “Bounds for Codes by Semidefinite Programming”, Geometry, topology, and mathematical physics. I, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 263, MAIK Nauka/Interperiodica, Moscow, 2008, 143–158; Proc. Steklov Inst. Math., 263 (2008), 134–149

Citation in format AMSBIB
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\paper Bounds for Codes by Semidefinite Programming
\inbook Geometry, topology, and mathematical physics.~I
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2008
\vol 263
\pages 143--158
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\pages 134--149
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Musin O.R., “Bounds for codes via semidefinite programming”, 2009 Information Theory and Applications Workshop, 2009, 234–236  mathscinet  isi
    2. Musin O.R., “Positive Definite Functions in Distance Geometry”, European Congress of Mathematics 2008, ed. Ran A. Riele H. Wiegerinck J., Eur. Math. Soc., 2010, 115–134  crossref  mathscinet  zmath  isi
    3. O. R. Musin, A. S. Tarasov, “Enumeration of irreducible contact graphs on the sphere”, J. Math. Sci., 203:6 (2014), 837–850  mathnet  crossref  mathscinet
    4. Okuda T., Yu W.-H., Eur. J. Comb., 53 (2016), 96–103  crossref  mathscinet  zmath  isi  scopus
    5. Musin O.R., “Towards a Proof of the 24-Cell Conjecture”, Acta Math. Hung., 155:1 (2018), 184–199  crossref  mathscinet  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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