Small minimal blocking sets in \(\text{PG}(2,q^3)\)
type: Item
instance of: scholarly article
title: Small minimal blocking sets in \(\text{PG}(2,q^3)\)
zbMATH Open document ID: 1001.51006
published in: European Journal of Combinatorics
publication date: 2002-12-09T00:00:00Z
review text: A blocking set \(B\) in PG\((2,q)\), \(q=p^n\), \(p\) prime, is called small if \(|B|<3(q+1)/2\). The exponent of \(B\) is the greatest integer \(e\) such that every line intersects \(B\) in 1 (mod \(p^e\)) points. The authors classify all minimal blocking sets in PG\((2,q^3)\), \(q=p^h\), \(p\geq 7\), with exponent \(e\geq h\), extending the results by \textit{O. Polverino} [Discrete Math. 208-209, 469-476 (1999; Zbl 0941.51008) and Des.\ Codes Cryprography 20, 319-324 (2000; Zbl 0969.51016)]. Such classification includes all minimal blocking sets of size at most \(q^3+q^2+q+1\).
reviewed by: Corrado Zanella
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 1740671
zbMATH Keywords: small blocking set
zbMATH Keywords: minimal blocking set
author: Olga Polverino
author: Leo Storme
MaRDI profile type: Publication
full work available at URL: eujc.2001.0545
OpenAlex ID: W1579657413
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DOI: 10.1006/EUJC.2001.0545
description: scientific article; zbMATH DE number 1740671