Hyperovals of $H(3,q^2)$ when $q$ is even

Antonio Cossidente; Oliver H. King; Giuseppe Marino

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arXiv · 1211.3649

Hyperovals of $H(3,q^2)$ when $q$ is even

Antonio Cossidente·Oliver H. King·Giuseppe Marino

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Abstract

For even $q$, a group $G$ isomorphic to $PSL(2,q)$ stabilizes a Baer conic inside a symplectic subquadrangle ${\cal W}(3,q)$ of ${\cal H}(3,q^2)$. In this paper the action of $G$ on points and lines of ${\cal H}(3,q^2)$ is investigated. A construction is given of an infinite family of hyperovals of size $2(q^3-q)$ of ${\cal H}(3,q^2)$, with each hyperoval having the property that its automorphism group contains $G$. Finally it is shown that the hyperovals constructed are not isomorphic to known hyperovals.

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BibTeX RIS

Antonio Cossidente, Oliver H. King, Giuseppe Marino. 2012-11-15. Hyperovals of $H(3,q^2)$ when $q$ is even. https://arxiv.org/abs/1211.3649

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