Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4665259 | Advances in Mathematics | 2015 | 9 Pages |
Abstract
A hyperoval in the projective plane P2(Fq)P2(Fq) is a set of q+2q+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)P2(Fq) are in one-to-one correspondence to polynomials with certain properties, called o-polynomials of FqFq. We classify o-polynomials of FqFq of degree less than 12q1/4. As a corollary we obtain a complete classification of exceptional o-polynomials, namely polynomials over FqFq that are o-polynomials of infinitely many extensions of FqFq.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Florian Caullery, Kai-Uwe Schmidt,