Complete caps in projective space which are disjoint from a subspace of codimension two
Abstract
Description
Working over the field of order 2 we consider those complete caps (maximal sets of points with no three collinear) which are disjoint from some codimension 2 subspace of projective space. We derive restrictive conditions which such a cap must satisfy in order to be complete. Using these conditions we obtain explicit descriptions of complete caps which do not meet every hyperplane in at least 5 points. In particular, we determine the set of cardinalities of all such complete caps in all dimensions.
13 pages. This is a corrected version of a paper that appeared in Finite Geometries, A. Blokhuis, J.W.P. Hirschfeld, D. Jungnickel and J.A. Thas, Editors, Kluwer Academic Publishing, Dordrecht, 2001, 347--361. The proof of Theorem 4.1 has been corrected as have the statements of Propositions 7.1 and 8.1
13 pages. This is a corrected version of a paper that appeared in Finite Geometries, A. Blokhuis, J.W.P. Hirschfeld, D. Jungnickel and J.A. Thas, Editors, Kluwer Academic Publishing, Dordrecht, 2001, 347--361. The proof of Theorem 4.1 has been corrected as have the statements of Propositions 7.1 and 8.1