On k-sets of class [0, q/2-1, q/2, q/2+ 1, q] in a plane of even order q

On q2/4-sets of type (0, q/4, q/2) in projective planes of order q=0(mod 4)

In this paper we investigate qz/4-sets of type (O,q/4,q/2) in projective planes of order q=O(mod4). These sets arise in the investigation of regular triples with respect to a hyperoval. Combinatorial properties of these sets are given and examples in Desarguesian projective planes are constructed.

Hyperovals of H(3, q2) when q is even

For even q, a group G isomorphic to PSL(2, q) stabilizes a Baer conic inside a symplectic subquadrangle W(3, q) of H(3, q2). In this paper the action of G on points and lines of H(3, q2) is investigated. A construction is given of an infinite family of hyperovals of size 2(q3−q) of H(3, q2), with each hyperoval having the property that its automorphism group contains G. Finally it is shown that...

On (q2+q+2, q+2)-arcs in the Projective Plane PG(2, q)

A (k; n)-arc in PG(2; q) is usually deened to be a set K of k points in the plane such that some line meets K in n points but such that no line meets K in more than n points. There is an extensive literature on the topic of (k; n)-arcs. Here we keep the same deenition but allow K to be a multiset, that is, permit K to contain multiple points. The case k = q 2 + q + 2 is of interest because it i...

Supplementary difference sets constructed from (q+1)st cyclotomic classes in GF(q2)

Minimal blocking sets of size q2+2 of Q(4, q), q an odd prime, do not exist

Consider the finite generalized quadrangle Q(4, q), q odd. An ovoid is a set O of points of Q(4, q) such that every line of the quadric contains exactly one point of O. A blocking set is a set B of points of Q(4, q) such that every line of the quadric contains at least one point of B. A blocking set B is called minimal if for every point p ∈ B, the set B \ {p} is not a blocking set. The GQ Q(4,...