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Small complete caps in PG(N, q), q even

✍ Scribed by Massimo Giulietti

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 191 KB
Volume: 15
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20131

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✦ Synopsis

Abstract

A new family of small complete caps in PG(N,q), q even, is constructed. Apart from small values of either N or q, it provides an improvement on the currently known upper bounds on the size of the smallest complete cap in PG(N,q): for N even, the leading term $q^{{N}\over{2}}$ is replaced by $\alpha q^{{N}\over{2}}$ with $\alpha \le {{1}\over{2}}$, for N odd the leading term $3q^{{N-1}\over{2}}$ is replaced by $\beta q^{{N-1}\over{2}}$ with $\beta \le {{5}\over{2}}$. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 420–436, 2007

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