On \(q^ 2/4\)-sets of type \((0,q/4,q/2)\) in projective planes of order \(q\equiv 0\pmod 4\)
type: Item
instance of: scholarly article
title: On \(q^ 2/4\)-sets of type \((0,q/4,q/2)\) in projective planes of order \(q\equiv 0\pmod 4\)
zbMATH Open document ID: 0803.51014
DOI: 10.1016/0012-365X(92)00509-P
published in: Discrete Mathematics
publication date: 1994-08-22T00:00:00Z
review text: Let \(H\) be a hyperoval in a finite projective plane \(\Pi\) of order \(q\); a triple of points \(x,y,z\) not in \(H\) is said to be regular if there is no point \(p\) such that all three lines \(px\), \(py\) and \(pz\) are exterior lines of \(H\). Regular triples of points were introduced by the first author (``Regular triples with respect to a hyperoval'', Ars Comb., to appear) who proved that they lead to sets of cardinality \(q^ 2/4\) and type \((0, q/4, q/2)\) in \(\Pi\); in particular, \(q\) has to be a multiple of 4. In the paper under review, the authors study such sets in general and provide two different classes of examples in \(\text{PG} (2,2^ h)\) for all \(h \geq 3\).
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 599968
zbMATH Keywords: hyperoval
zbMATH Keywords: intersection numbers
zbMATH Keywords: projective plane
author: Antonio Maschietti
author: Grazia Migliori
reviewed by: Dieter Jungnickel
MaRDI profile type: Publication
cites work: Q3851217
cites work: Q4842740
cites work: Hyperovals and Hadamard designs
cites work: Q3272923
cites work: Q3331226
cites work: Q5524221
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description: scientific article; zbMATH DE number 599968