On the classification of hyperovals

A hyperoval in the projective plane P2(Fq) is a set of q+2 points no three of which are collinear. Hyperovals have been studied extensively since the 1950s with the ultimate goal of establishing a complete classification. It is well known that hyperovals in P2(Fq) are in one-to-one correspondence to...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2015-10, Vol.283, p.195-203
Main Authors: Caullery, Florian, Schmidt, Kai-Uwe
Format: Article
Language:English
Subjects:
Classification
Finite projective plane
Hyperoval
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Summary:A hyperoval in the projective plane P2(Fq) is a set of q+2 points no three of which are collinear. Hyperovals have been studied extensively since the 1950s with the ultimate goal of establishing a complete classification. It is well known that hyperovals in P2(Fq) are in one-to-one correspondence to polynomials with certain properties, called o-polynomials of Fq. We classify o-polynomials of Fq of degree less than 12q1/4. As a corollary we obtain a complete classification of exceptional o-polynomials, namely polynomials over Fq that are o-polynomials of infinitely many extensions of Fq.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2015.07.016