Small blocking sets in \(PG(2,p^3)\)
type: Item
instance of: scholarly article
title: Small blocking sets in \(PG(2,p^3)\)
zbMATH Open document ID: 0969.51016
DOI: 10.1023/A:1008330310213
author: Olga Polverino
published in: Designs, Codes and Cryptography
publication date: 2001-09-27T00:00:00Z
review text: A blocking set in a projective plane is a set of points which intersects every line. A blocking set containing a line is called trivial. A blocking set in a plane of order \(q\) is called small if it contains at most \(3(q+1)/2\) points. If a nontrivial blocking set \(B\) in a plane of order \(q\) contains \(q + N\) points, then each line intersects \(B\) in at most \(N\) points, and if this bound is attained then \(B\) is called of Redei type. The author proves that for \(p \geq 7\) every small minimal blocking set in \(PG(2,q^3)\) is of Redei type. A similar result is known to be true for \(r = 2\), whereas for \(r \geq 4\) there are counterexamples.
reviewed by: Norbert Knarr
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 1515346
zbMATH Keywords: small minimal blocking set
zbMATH Keywords: Redei type
MaRDI profile type: Publication
full work available at URL: a:1008330310213
OpenAlex ID: W1982854113
description: scientific article; zbMATH DE number 1515346