Intersection of arcs and normal rational curves in spaces of even characteristic
type: Item
instance of: scholarly article
title: Intersection of arcs and normal rational curves in spaces of even characteristic
zbMATH Open document ID: 0821.51006
DOI: 10.1007/BF01226864
published in: Journal of Geometry
publication date: 1994-12-08T00:00:00Z
review text: The \((k + 1)\)-arcs \(K\) in \(PG(n,q)\), \(q\) even, which have \(k\) points in common with a given rational curve \(L\) of \(PG(n,q)\) are studied in detail. It is proved that, for \(q \geq q_ 0\), \(| K \cap L| \leq (q + 4)/2\) when \(n = 3\) and \(| K \cap L | \leq (q + 2)/2\) when \(4 \leq n \leq 0.09q + 2.59\), improving previous results. This is used to give a complete characterization of arcs of \(PG(n,q)\), \(q\) even and \(q \geq q_ 0\), having at least \(0.41(q + 1)\) or \(0,41q + n - 1.59\) points in common with \(L\) according to \(n = 3\) or \(4 \leq n \leq 0.09q + 2.59\).
reviewed by: Giustina Pica
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 700405
zbMATH Keywords: \(k\)-arcs
author: Leo Storme
author: Tamás Szőnyi
MaRDI profile type: Publication
cites work: Subset sums
cites work: Applications of line geometry over finite fields I: The twisted cubic
cites work: Q3851217
cites work: Q3694152
cites work: An elementary proof and an extension of Thas' theorem on k-arcs
cites work: A construction of non-Reed-Solomon type MDS codes
cites work: Q3238824
cites work: Q5334400
cites work: On Certain Sets of Integers
cites work: Q5589782
cites work: On MDS extensions of generalized Reed- Solomon codes
cites work: Q3357797
cites work: Completeness of normal rational curves
cites work: Q5342900
cites work: Q5582819
description: scientific article; zbMATH DE number 700405