On smallest covers of finite projective spaces
type: Item
instance of: scholarly article
title: On smallest covers of finite projective spaces
zbMATH Open document ID: 0896.51010
author: J. Eisfeld
published in: Archiv der Mathematik
publication date: 1997-06-24T00:00:00Z
review text: Let \({\mathcal P}= \text{PG} (d,q)\) be a projective space of dimension \(d\) and order \(q\). A set \({\mathcal S}\) of \(t\)-dimensional subspaces of \({\mathcal P}\) is called a \(t\)-cover of \({\mathcal P}\) if and only if every point of \({\mathcal P}\) is contained in at least one element of \({\mathcal S}\). \textit{A. Beutelspacher} [J. Geom. 12, 10-16 (1979; Zbl 0386.05023)] proved that the cardinality of such a \(t\)-cover is at least \(| {\mathcal S} |= q^{r+1} \cdot {q^{k(t+1)} -1\over q^{t+1} -1}+1\). The author sketches Beutelspacher's construction and proves that all examples of minimal cardinality ``look like'' the examples given by Beutelspacher.
Mathematics Subject Classification ID: 51E23
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51A05
zbMATH DE Number: 1026249
zbMATH Keywords: \(t\)-cover
zbMATH Keywords: projective space
reviewed by: Pavel Burda
MaRDI profile type: Publication
full work available at URL: s000130050034
OpenAlex ID: W2034468195
cites work: A characterization of flat spaces in a finite geometry and the uniqueness of the hamming and the MacDonald codes
cites work: Q3851217
DOI: 10.1007/S000130050034
description: scientific article; zbMATH DE number 1026249