Characterising elliptic solids of Q(4,q), q even

2019/06/04 by S. G. Barwick, Alice M. W. Hui, Barwick, S. G. +3 · 1 citation
Mathematics · Computer Science · #Finite Group Theory Research #Limits and Structures in Graph Theory #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.1906.03985

Abstract

Let E be a set of solids (hyperplanes) in PG(4,q), q even, q>2, such that every point of PG(4,q) lies in either 0, \frac12q³ or \frac12(q³-q²) solids of E, and every plane of PG(4,q) lies in either 0, \frac12q or q solids of E. This article shows that E is either the set of solids that are disjoint from a hyperoval, or the set of solids that meet a non-singular quadric Q(4,q) in an elliptic quadric.

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• Characterization of non-singular hyperplanes of H(s,q²) in P G(s, q²)

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