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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 263, Pages 143–158 (Mi tm789)  
This article is cited in 9 scientific papers (total in 9 papers)

Bounds for Codes by Semidefinite Programming

O. R. Musin

Department of Mathematics, University of Texas at Brownsville
Full-text PDF (239 kB) Citations (9)
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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.
Received in August 2008
English version:
Proceedings of the Steklov Institute of Mathematics, 2008, Volume 263, Pages 134–149
DOI: https://doi.org/10.1134/S0081543808040111
Bibliographic databases:
UDC: 519.14+519.72
Language: English
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, Trudy 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 Trudy Mat. Inst. Steklova
\yr 2008
\vol 263
\pages 143--158
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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Linking options:
  • https://www.mathnet.ru/eng/tm789
  • https://www.mathnet.ru/eng/tm/v263/p143
    • This publication is cited in the following 9 articles:
    1. Xavier Emery, Ana Paula Peron, Emilio Porcu, “A catalogue of nonseparable positive semidefinite kernels on the product of two spheres”, Stoch Environ Res Risk Assess, 37:4 (2023), 1497  crossref
    2. Musin O.R., “Towards a Proof of the 24-Cell Conjecture”, Acta Math. Hung., 155:1 (2018), 184–199  crossref  mathscinet  isi  scopus
    3. Konrad J. Swanepoel, Bolyai Society Mathematical Studies, 27, New Trends in Intuitive Geometry, 2018, 407  crossref
    4. Oleg R. Musin, Bolyai Society Mathematical Studies, 27, New Trends in Intuitive Geometry, 2018, 321  crossref
    5. Okuda T., Yu W.-H., Eur. J. Comb., 53 (2016), 96–103  crossref  mathscinet  zmath  isi  scopus
    6. 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
    7. 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
    8. Musin O.R., “Bounds for codes via semidefinite programming”, 2009 Information Theory and Applications Workshop, 2009, 234–236  mathscinet  isi
    9. O.R. Musin, 2009 Information Theory and Applications Workshop, 2009, 237  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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