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

Authors:
S. Boumova;P. Boyvalenkov;M. Stoyanova
Affiliations:
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria;Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria;Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria
Venue:
Problems of Information Transmission
Year:
2009

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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.