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Polynomials for hyperovals of Desarguesian planes

Published online by Cambridge University Press:  09 April 2009

Christine M. O'keefe
The University of Western AustraliaNedlands, W. A. 6009, Australia
Tim Penttila
The University of Western AustraliaNedlands, W. A. 6009, Australia
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This paper studies o-polynomials, that is, polynomials which represent 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, 16 and 32. Exploratory computer searches for o-polynomials for fields of small orders greater than 16 are reported.

MSC classification

Research Article
Copyright © Australian Mathematical Society 1991


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