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A method for proving nonexistence of spherical designs of odd strength and odd cardinality

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Abstract

We combine polynomial techniques with some geometric arguments to obtain restrictions of the structure of spherical designs with fixed odd strength and odd cardinality. Our bounds for the extreme inner products of such designs allow us to prove nonexistence results in many cases. Applications are shown for 7-designs.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    S. Boumova & P. Boyvalenkov

  2. Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria

    M. Stoyanova

Authors
  1. S. Boumova
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  2. P. Boyvalenkov
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  3. M. Stoyanova
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Correspondence to S. Boumova.

Additional information

Original Russian Text © S. Boumova, P. Boyvalenkov, M. Stoyanova, 2009, published in Problemy Peredachi Informatsii, 2009, Vol. 45, No. 2, pp. 41–55.

Supported in part by the Bulgarian NSF under Contract MM-1405/2004 and the SF of Sofia University under Contract 171/05.2008.

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Boumova, S., Boyvalenkov, P. & Stoyanova, M. A method for proving nonexistence of spherical designs of odd strength and odd cardinality. Probl Inf Transm 45, 110–123 (2009). https://doi.org/10.1134/S0032946009020033

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  • DOI: https://doi.org/10.1134/S0032946009020033

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