Partial ovoids in classical finite polar spaces
type: Item
instance of: scholarly article
title: Partial ovoids in classical finite polar spaces
zbMATH Open document ID: 1052.51006
published in: Designs, Codes and Cryptography
publication date: 2004-08-19T00:00:00Z
review text: A set \(O\) of points meeting exactly once every generator of a polar space \(P\) is called an ovoid of \(P\). A partial ovoid of \(P\) is a set meeting every generator of \(P\) at most once. There are several well-known results on the nonexistence of ovoids in polar spaces; for instance \(Q^{-}(2n+1,q)\), \(W(2n+1,q)\) and \(H(2n,q^2)\) for \(n\geq 2\) do not admit any ovoid. It is then most interesting to try to determine the maximum size of a partial ovoid contained in such spaces or, at least, to provide good upper bounds. In the first part of this paper, the author proves two inductive bounds on the size of an ovoid of \(Q^{-}(2n+1,q)\) and of \(W(2n+1,q)\) which improve (at least for large \(p\)) the results already known. In the second part of the paper a simple proof of the nonexistence of ovoids in \(H(2n+1,q^2)\) when \(n>q^3\) is presented.
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 51A50
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 2093317
zbMATH Keywords: partial ovoids
zbMATH Keywords: polar spaces
author: Andreas Klein
reviewed by: Luca Giuzzi
MaRDI profile type: Publication
full work available at URL: b:desi.0000015885.23333.ca
OpenAlex ID: W1964404040
DOI: 10.1023/B:DESI.0000015885.23333.CA
description: scientific article; zbMATH DE number 2093317