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

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dc.creatorDavydov, Alexander A.
dc.creatorGiulietti, Massimo
dc.creatorMarcugini, Stefano
dc.creatorPambianco, Fernanda
dc.date2009-01-04
dc.date.accessioned2026-07-07T12:24:31Z
dc.date.available2026-07-07T12:24:31Z
dc.descriptionSome 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 $PG(N,q),$ $N\geq 4,$ for all $q\geq 2^{3}.$ In particular, substantial improvements are obtained for infinite values of $q$ square, including $ q=2^{2Cm},$ $C\geq 5,$ $m\geq 3;$ for $q=2^{Cm},$ $C\geq 5,$ $m\geq 9,$ with $C,m$ odd; and for all $q\leq 2^{18}.$
dc.identifierhttps://arxiv.org/abs/0901.0367
dc.identifierhttp://arxiv.org/abs/0901.0367
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/214350
dc.subjectCombinatorics
dc.subject51E22
dc.titleNew inductive constructions of complete caps in $PG(N,q)$, $q$ even
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