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≥2^3. 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≤2^18.
New inductive constructions of complete caps in PG(N,q), q even
GIULIETTI, Massimo;MARCUGINI, Stefano;PAMBIANCO, Fernanda
2010
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≥2^3. 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≤2^18.File in questo prodotto:
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