A family of small complete caps in \(\text{PG}(n,2)\)
type: Item
instance of: scholarly article
title: A family of small complete caps in \(\text{PG}(n,2)\)
zbMATH Open document ID: 1030.51010
DOI: 10.1016/S0195-6698(03)00067-2
author: Jeffrey J. E. Imber
author: David Wehlau
published in: European Journal of Combinatorics
publication date: 2003-08-25T00:00:00Z
review text: A cap of the projective space \(P=\text{PG}(n, q)\) is a set of points no three of them collinear. A cap is called complete if it is not contained in any cap of higher cardinality. Imber and Wehlau construct two families of complete arcs of cardinality \(24 (2^{(n-6)/2}) - 3\) for \(n\) even and \(16 (2^{(n-5)/2}) - 3\) for \(n\) odd. For their construction the black/white lift introduced by \textit{A. A. Bruen} and \textit{D. L. Wehlau} [J. Comb. Theory, Ser. A 94, 196-202 (2001; Zbl 0990.94032)] is used. Note that the smallest known complete arcs are of cardinality \(23 (2^{(n-6)/2}) - 3\) for \(n\) even and \(n \geq 10\) and of cardinality \(15 (2^{(n-5)/2}) - 3\) for \(n\) odd and \(n \geq 9\).
reviewed by: Johannes Ueberberg
Mathematics Subject Classification ID: 51E22
zbMATH DE Number: 1970581
zbMATH Keywords: cap
zbMATH Keywords: code
zbMATH Keywords: complete arcs
MaRDI profile type: Publication
cites work: New codes from old; a new geometric construction
cites work: Linear codes with covering radius 2 and other new covering codes
description: scientific article; zbMATH DE number 1970581