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On the classification of hyperovals
- Publication Year :
- 2014
-
Abstract
- A hyperoval in the projective plane $\mathbb{P}^2(\mathbb{F}_q)$ 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 $\mathbb{P}^2(\mathbb{F}_q)$ are in one-to-one correspondence to polynomials with certain properties, called o-polynomials of $\mathbb{F}_q$. We classify o-polynomials of $\mathbb{F}_q$ of degree less than $\frac12q^{1/4}$. As a corollary we obtain a complete classification of exceptional o-polynomials, namely polynomials over $\mathbb{F}_q$ that are o-polynomials of infinitely many extensions of $\mathbb{F}_q$.
- Subjects :
- Mathematics - Combinatorics
05B25, 11T06, 51E20
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1403.2880
- Document Type :
- Working Paper