\(k\)-arcs, hyperovals, partial flocks and flocks
type: Item
instance of: scholarly article
title: \(k\)-arcs, hyperovals, partial flocks and flocks
zbMATH Open document ID: 0862.51008
DOI: 10.1023/A:1027398110064
published in: Designs, Codes and Cryptography
publication date: 1997-05-29T00:00:00Z
review text: This is a survey of results on the objects of the title. A \(k\)-arc in a projective plane is a set of \(k\) points, no three of which are collinear. In a finite projective plane of order \(q\), an oval is a \(k\)-arc with \(k= q+1\). If \(k= q+2\), the \(k\)-arc is a hyperoval. Hyperovals can exist only if \(n\) is even. In all cases, the projective plane is the Desarguesian projective plane \(PG(2,q)\). All known hyperovals are listed. Let \(k\) be a quadratic cone in \(PG(3,q)\). A partition of the points of \(k\) other than the vertex is a flock. A partial flock is a set of disjoint conics on the non-vertex points of \(k\). The author summarizes known relations between \(k\)-arcs and partial flocks.
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 51E22
zbMATH DE Number: 934922
zbMATH Keywords: \(k\)-arc
zbMATH Keywords: projective plane
zbMATH Keywords: hyperoval
zbMATH Keywords: flock
zbMATH Keywords: partial flock
author: Joseph A. Thas
reviewed by: Theodore G. Ostrom
MaRDI profile type: Publication
full work available at URL: a:1027398110064
OpenAlex ID: W1984637850
description: scientific article; zbMATH DE number 934922