New inductive constructions of complete caps in PG(N,q), q even

2009/01/04 by Alexander A. Davydov, Davydov, Alexander A., Massimo Giulietti +5
Mathematics · #51E22 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:51E22

paper · pdf · doi:10.48550/arxiv.0901.0367

arxiv created 2009/01/04 · arxiv updated 2009/12/01

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 paper 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=2^2Cm, C≥ 5, m≥ 3; for q=2^Cm, C≥ 5, m≥ 9, with C,m odd; and for all q≤ 2¹⁸.

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