On the intersection of two regular hyperovals in projective planes of even order

Abstract

A k-arc K in a projective plane PG(2, q) of order q is a set of k distinct points such that any line in the plane meets K in at most two points. For considering some applications, such as optical orthogonal codes, we are interested in the number of intersection points between two regular hyperovals, which are (q + 2) -arcs consisting of a conic and its nucleus when q is even. In this paper, the number of intersection points of two regular hyperovals can be classified according to how the corresponding conics intersect.

Keywords:

• conic
• nucleus
• regular hyperoval
• optical orthogonal code

2000 Mathematics Subject Classification:

• 51E21