On the embedding of \((k,p)\)-arcs in maximal arcs
type: Item
instance of: scholarly article
title: On the embedding of \((k,p)\)-arcs in maximal arcs
zbMATH Open document ID: 0964.51010
DOI: 10.1023/A:1008366025930
published in: Designs, Codes and Cryptography
publication date: 2001-01-01T00:00:00Z
review text: A \((k,n)\)-arc in a projective plane of order \(q\) is a set of \(k\) points no \(n+1\) on a line. The author proves that every \((k,p)\)-arc in \(\text{PG}(2,q)\), \(q=p^h\), \(p\) prime and \(k \geq qp-q+p-\frac{1}{2}{\root 4\of q}\), can be extended to a maximal arc. Using the nonexistence of maximal arcs for \(p > 2\) [\textit{S. Ball, A. Blokhuis} and \textit{F. Mazzocca}, Combinatorica 17, No. 1, 31-41 (1997; Zbl 0880.51003)], an upper bound for the size of a \((k,p)\)-arc is obtained.
reviewed by: Bart De Bruyn
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 1548362
zbMATH Keywords: maximal arcs
zbMATH Keywords: \((k,n)\)-arc
author: Tamás Szőnyi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1548362