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

Preprint

2 March 2004

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0403031

Abstract

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.

Keywords

PROJECTIVE SPACE
CODIMENSION TWO
COMPLETE CAPS
TWO WORKING
COLLINEAR
SUBSPACE
DISJOINT

All Related Versions

Version 1, 2004-03-02, ArXiv

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