On the intersection of two regular hyperovals in projective planes of even order
type: Item
instance of: scholarly article
title: On the intersection of two regular hyperovals in projective planes of even order
zbMATH Open document ID: 1142.51009
author: Nobuko Miyamoto
author: Satoshi Shinohara
published in: AKCE International Journal of Graphs and Combinatorics
publication date: 2008-02-05T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 94B60
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 5232105
zbMATH Keywords: conic
zbMATH Keywords: nucleus
zbMATH Keywords: regular hyperoval
zbMATH Keywords: optical orthogonal code
reviewed by: Leo Storme
MaRDI profile type: Publication
description: scientific article