Classification of hyperovals in \(PG(2,32)\)
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'].
scientific article; zbMATH DE number 621998
scientific article