On the intersection of two regular hyperovals in projective planes of even order
A \textit{\(k\)-arc} in the projective plane \(\mathrm{PG}(2,q)\) of order \(q\) is a set of \(k\) points, such that no three points are collinear. The projective plane \(\mathrm{PG}(2,q)\), \(q\) even, has \((q+2)\)-arcs. The \((q+2)\)-arcs in \(\mathrm{PG}(2,q)\), \(q\) even, are called \textit{hyperovals}. The classical example of a hyperoval in \(\mathrm{PG}(2,q)\), \(q\) even, is the \textit{regular} hyperoval, i.e., the union of a conic and its nucleus. For applications, such as optical orthogonal codes, the authors discuss the intersections of two regular hyperovals. A similar article discussing the intersection of regular hyperovals was written by \textit{J. M. McQuillan} [Des. Codes Cryptography 20, No.~1, 65--71 (2000; Zbl 0978.51004)]. There the regular hyperovals are called hyperconics.
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