Designs over finite fields
type: Item
instance of: scholarly article
title: Designs over finite fields
zbMATH Open document ID: 0627.51013
DOI: 10.1007/BF00150939
author: Simon Thomas
published in: Geometriae Dedicata
publication date: 1987-01-01T00:00:00Z
review text: Let F be a finite field. A t-(n,k,\(\lambda)\)-design over F is a collection of k-dimensional subspaces (``blocks'') of \(F^ n\) with the property that every t-space is contained in exactly \(\lambda\) blocks. This generalizes the notion of an ordinary t-design. Prior to the paper under review, no non-trivial examples are known for \(t\geq 2\). (Spreads yield examples for \(t=1.)\) The author constructs a 2-(n,3,7)-design over GF(2) whenever \(\gcd (n,6)=1\). For \(n\geq 7\), these are non-trivial.
reviewed by: Dieter Jungnickel
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 51E05
zbMATH DE Number: 4019873
zbMATH Keywords: finite field
zbMATH Keywords: projective space
zbMATH Keywords: design
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00150939
OpenAlex ID: W2086724086
description: scientific article; zbMATH DE number 4019873