A family of m-ovoids of parabolic quadrics

2015/09/02 by Tao Feng, Feng, Tao, Koji Momihara +3
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1509.00550

openalex publication_date 2015/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a family of ((q-1))/(2)-ovoids of Q(4,q), the parabolic quadric of \textupPG(4,q), for q≡ 3\pmod 4. The existence of ((q-1))/(2)-ovoids of Q(4,q) was only known for q=3, 7, or 11. Our construction provides the first infinite family of ((q-1))/(2)-ovoids of Q(4,q).Along the way, we also give a construction of (q+1)/(2)-ovoids in Q(4,q) for q≡ 1\pmod 4.

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