J Austral Math Soc Ser A 51 pp436--447, 1991.

Polynomials for Hyperovals of Desarguesian Planes

Christine M. O'Keefe and Tim Penttila

Abstract

This paper studies o-polynomials, that is, polynomials hyperovals in Desarguesian projective planes of even order. We present theoretical restrictions on the form that o-polynomials can have, and we determine the number of o-polynomials corresponding to each of the known classes of hyperovals (other than Cherowitzo's). We use this to give the number of known o-polynomials for the fields of orders 4, 8, 6 and 32. Exploratory computer searches for o-polynomials for fields of small orders greater than 16 are reported.

1991 AMS Subject Classification: 51E20

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Authors

Christine M. O'Keefe

Tim Penttila

The University of Western Australia, Nedlands, W. A. 6009, Australia.