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Polynomials for hyperovals of Desarguesian planes

Part of: Linear incidence geometry Geometry

Published online by Cambridge University Press:  09 April 2009

Christine M. O'keefe  and
Tim Penttila
Christine M. O'keefe
Affiliation:
The University of Western AustraliaNedlands, W. A. 6009, Australia
Tim Penttila
Affiliation:
The University of Western AustraliaNedlands, W. A. 6009, Australia
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Abstract

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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

Secondary: 51A20: Configuration theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 3 , December 1991 , pp. 436 - 447
Copyright
Copyright © Australian Mathematical Society 1991

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