Covering pairs by q2 + q + 1 sets

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

ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS

Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...

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,...

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.

On the covering of pairs by quadruples