Hyperovals of H(3,q²) when q is even

2012/11/15 by Antonio Cossidente, Cossidente, Antonio, Oliver H. King +3
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #math.CO

paper · pdf · doi:10.48550/arxiv.1211.3649

Submitted

arxiv created 2012/11/15 · openalex publication_date 2012/11/15 · arxiv updated 2012/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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,q²). In this paper the action of G on points and lines of \cal H(3,q²) is investigated. A construction is given of an infinite family of hyperovals of size 2(q³-q) of \cal H(3,q²), 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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