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New inductive constructions of complete caps in PG ( N, q ), q even
Author(s) -
Davydov Alexander A.,
Giulietti Massimo,
Marcugini Stefano,
Pambianco Fernanda
Publication year - 2010
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20230
Subject(s) - mathematics , combinatorics , projective plane , square (algebra) , plane (geometry) , discrete mathematics , geometry , correlation
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 2 Cm , C ≥5, m ≥3; for q =2 Cm , C ≥5, m ≥9, with C , m odd; and for all q ≤2 18 . © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 177–201, 2010