On \((q+t,t)\)-arcs of type \((0,2,t)\)
type: Item
instance of: scholarly article
title: On \((q+t,t)\)-arcs of type \((0,2,t)\)
zbMATH Open document ID: 1029.51011
DOI: 10.1023/A:1024152424893
author: András Gács
author: Zsuzsa Weiner
published in: Designs, Codes and Cryptography
publication date: 2003-08-21T00:00:00Z
review text: A \((q + t, t)\)-arc of type \((0, 2, t)\) is a set of \(q + t\) points of the projective plane \(\text{PG}(2, q)\) such that every line meets it in \(0\), \(2\) or \(t\) points. In 1990, \textit{G. Korchmáros} and \textit{F. Mazzocca} [Math. Proc. Comb. Philos. Soc. 108, 445-459 (1990; Zbl 0716.51010)] constructed an infinite series of examples of \((q + t, t)\)-arcs of type \((0, 2, t)\). In the paper under review, the authors give a more general construction for \((q + t, t)\)-arcs of type \((0, 2, t)\) which includes those of Korchmáros and Mazzocca, and which gives new inifinite series of examples, too. They give both a geometric and an algebraic way of constructing these arcs.
reviewed by: V. Napolitano
Mathematics Subject Classification ID: 51E14
zbMATH DE Number: 1968862
zbMATH Keywords: arcs
zbMATH Keywords: hyperoval
zbMATH Keywords: \(t\)-nucleus
zbMATH Keywords: Rédei polynomial
MaRDI profile type: Publication
full work available at URL: a:1024152424893
OpenAlex ID: W1543840521
description: scientific article; zbMATH DE number 1968862