Intersection-sets in \(PG(n,2)\)
type: Item
instance of: scholarly article
title: Intersection-sets in \(PG(n,2)\)
zbMATH Open document ID: 0917.51006
DOI: 10.1016/S0378-3758(96)00161-9
author: Lucien Haddad
author: Aiden A. Bruen
author: David Wehlau
published in: Journal of Statistical Planning and Inference
publication date: 1997-09-22T00:00:00Z
review text: A subset \(X\) of \(PG(n,2)\) is called independent if it is line-free, and a set \(C\) is said to be an \(r\)-intersection-set of \(PG(n,2)\) if \(| C\cap K|\geq r\), for all hyperplanes \(K\). In the paper under review line-free intersection-sets of \(PG(n,2)\) are examined, and their incidence equations are described. The authors construct a line-free subset \(X_n\) of \(PG(n,2)\), for every \(n\geq 3\), which meets every hyperplane in at least \(2^{n-3}\) points. For \(n=3,4,5\), the set \(X_n\) is the unique (up to isomorphism) set having these two properties. Further results on \(r\)-intersection-sets in \(PG(n,2)\), \(n=5,6\) are also given.
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 1057360
zbMATH Keywords: caps
zbMATH Keywords: codes
zbMATH Keywords: 2-blocks
zbMATH Keywords: projective space
zbMATH Keywords: blocking sets
zbMATH Keywords: line-free intersection-sets
reviewed by: Antonio Cossidente
MaRDI profile type: Publication
cites work: Q3996173
cites work: Polynomial multiplicities over finite fields and intersection sets
cites work: 5‐chromatic steiner triple systems
cites work: Q3960715
cites work: Q5620610
full work available at URL: s0378-3758(96)00161-9
OpenAlex ID: W1979521169
description: scientific article; zbMATH DE number 1057360