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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



On tight spherical designs

Authors: G. Nebe and B. Venkov
Original publication: Algebra i Analiz, tom 24 (2012), nomer 3.
Journal: St. Petersburg Math. J. 24 (2013), 485-491
MSC (2010): Primary 05B30, 51E30
Published electronically: March 21, 2013
MathSciNet review: 3014131
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X$ be a tight $ t$-design of dimension $ n$, and let $ t=5$ or $ t=7$ (the open cases). An investigation of the lattice generated by $ X$ by using arithmetic theory of quadratic forms allows one to exclude infinitely many values of $ n$.

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Additional Information

G. Nebe
Affiliation: Lehrstuhl D für Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany

B. Venkov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, Saint Petersburg 191023, Russia

Keywords: tight $t$-design, quadratic form
Received by editor(s): November 1, 2011
Published electronically: March 21, 2013
Additional Notes: Boris Venkov died in November 2011 before we could finish this paper
Article copyright: © Copyright 2013 American Mathematical Society

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