Classification of spreads of Tits quadrangles of order 64

2023/05/05 by Giusy Monzillo, Monzillo, Giusy, Tim Penttila +3
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2305.03346

openalex publication_date 2023/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Brown et al. provide a representation of a spread of the Tits quadrangle T₂(\mathcal O), \mathcal O an oval of \mathrm PG(2,q), q even, in terms of a certain family of q ovals of \mathrm PG(2,q). By combining this representation with the Vandendriessche classification of hyperovals in \mathrm PG(2,64) and the classification of flocks of the quadratic cone in \mathrm PG(3,64), recently given by the authors, in this paper, we classify all the spreads of T₂(\mathcal O), \mathcal O an oval of \mathrm PG(2,64), up to equivalence. These complete the classification of spreads of T₂(\mathcal O) for q≤ 64.

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