On \(k\)-arcs covering a line in finite projective planes.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1065.51007
author: Siaw-Lynn Ng
author: Peter R. Wild
publication date: 2005-07-20T00:00:00Z
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 1600990
zbMATH Keywords: covering arc
zbMATH Keywords: projective plane
zbMATH Keywords: affine plane
zbMATH Keywords: perfect hash family
MaRDI profile type: Publication
title: On \(k\)-arcs covering a line in finite projective planes.
published in: Ars Combinatoria
review text: Consider a line in a \(\text{PG}(2,q)\). A \(k\)-arc covers the line, if every point of the line lies on a secant of the arc. The authors show that there exist covering \(k\)-arcs with \(k\) approximately \(2\sqrt {\mathstrut q}\), prove \(k \geq (1+\sqrt {8q+9})/2\) and establish when the equality holds. They also connect the notion of covering arcs to the notion of perfect hash families.
reviewed by: Aleš Drápal
description: scientific article; zbMATH DE number 1600990