Complete caps in projective space which are disjoint from a subspace of codimension two

Details Complete caps in projective space which are disjoint from a subspace of codimension two Complete caps in projective space which are disjoint from a subspace of codimension two

2004-03-02

arxiv.org/abs/math/0403031v1

Mathematics

Combinatorics

13 pages. This is a corrected version of a paper that appeared in Finite Geometries, A. Blokhuis, J.W.P. Hirschfeld, D. Jungni

Scientific paper

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.

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