Three families of multiple blocking sets in Desarguesian projective planes of even order
type: Item
instance of: scholarly article
title: Three families of multiple blocking sets in Desarguesian projective planes of even order
zbMATH Open document ID: 1288.51005
author: Anton Betten
author: Eun Ju Cheon
author: Seon Jeong Kim
author: Tatsuya Maruta
published in: Designs, Codes and Cryptography
publication date: 2013-05-30T00:00:00Z
review text: If \(H\) is a hyperoval of \(\mathrm{PG}(2,2^h),\) denote with \(\mathcal E\) the set of all lines external to \(H\) and with \(\mathcal S\) the set of all lines secant to \(H\). Using such sets of lines, the authors define three different families of lines \({\mathcal A}_1,\) \({\mathcal A}_2\) \({\mathcal A}_3\) of \(\mathrm{PG}(2,2^h)\) whose dual is a \(k\)-arc. As the complement of a \(k\)-arc is an \(s\)-fold blocking set with \(s+k=2^h+1,\) they construct three examples of multiple blocking sets. The first and the third construction only apply to translation hyperovals.
reviewed by: Guglielmo Lunardon
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 05E18
Mathematics Subject Classification ID: 20B40
zbMATH DE Number: 6168449
zbMATH Keywords: blocking set
zbMATH Keywords: projective plane
zbMATH Keywords: arc
zbMATH Keywords: hyperoval
MaRDI profile type: Publication
full work available at URL: s10623-012-9634-1
OpenAlex ID: W2010611757
cites work: Multiple Blocking Sets and Arcs in Finite Planes
cites work: On multiple nuclei and a conjecture of Lunelli and Sce
cites work: Q4370894
cites work: Q3260067
DOI: 10.1007/S10623-012-9634-1
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description: scientific article; zbMATH DE number 6168449