Classification of hyperovals in \(PG(2,32)\)
type: Item
instance of: scholarly article
title: Classification of hyperovals in \(PG(2,32)\)
zbMATH Open document ID: 0805.51005
DOI: 10.1007/BF01222672
author: Tim Penttila
author: Gordon Royle
published in: Journal of Geometry
publication date: 1994-09-13T00:00:00Z
review text: A hyperoval in the desarguesian projective plane \(\text{PG}(2,q)\), \(q\) even, is a set of \(q+2\) points no three of which lie on a line. This interesting paper starts with a list of the twelve families of hyperovals known at the time the paper was written (early in 1992) and then describes an exhaustive computer search for the hyperovals in PG(2, 32), with the result that there are exactly six classes of hyperovals up to isomorphism, and they were all previously known. This extends the orders for which we have complete knowledge, as previously all the hyperovals in \(\text{PG}(2,q)\) for even \(q\) less than 32 had been determined. Since the writing of this paper (early 1992) several sporadic examples of hyperovals have been found in larger planes [see the authors, `On hyperovals in small projective planes'] along with a new infinite family, the so-called Subiaco hyperovals [see \textit{W. Cherowitzo}, the first author, \textit{I. Pinneri} and the second author, `Flocks and ovals'; see also: the reviewer, the first author and \textit{I. Pinneri}, `Isomorphisms between Subiaco \(q\)-clan geometries'].
reviewed by: Stanley E. Payne
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 621998
zbMATH Keywords: finite Desarguesian projective plane
zbMATH Keywords: hyperovals
describes a project that uses: nauty
MaRDI profile type: Publication
cites work: Q3796299
cites work: Q3312809
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full work available at URL: https://doi.org/10.1007/bf01222672
OpenAlex ID: W2008146298
description: scientific article; zbMATH DE number 621998