COMPLETE CAPS IN PROJECTIVE SPACE WHICH ARE DISJOINT FROM A SUBSPACE OF CODIMENSION TWO

Working over the field of order 2 we consider those complete caps 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.