New inductive constructions of complete caps in PG(N,q), q even |
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| Authors: | Alexander A. Davydov Massimo Giulietti Stefano Marcugini Fernanda Pambianco |
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| Affiliation: | 1. Institute for Information Transmission Problems, Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, GSP‐4, Moscow 127994, Russian Federation;2. Dipartimento di Matematica e Informatica, Universitá degli Studi di Perugia, Via Vanvitelli 1, Perugia 06123, Italy |
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| Abstract: | Some new families of small complete caps in PG(N, q), q even, are described. By using inductive arguments, the problem of the construction of small complete caps in projective spaces of arbitrary dimensions is reduced to the same problem in the plane. The caps constructed in this article provide an improvement on the currently known upper bounds on the size of the smallest complete cap in PG(N, q), N≥4, for all q≥23. In particular, substantial improvements are obtained for infinite values of q square, including q=22Cm, C≥5, m≥3; for q=2Cm, C≥5, m≥9, with C, m odd; and for all q≤218. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 177–201, 2010 |
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| Keywords: | projective space complete cap complete arc |
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