Projective geometric codes
type: Item
instance of: scholarly article
title: Projective geometric codes
zbMATH Open document ID: 1026.94019
author: Bhaskar Bagchi
author: S. P. Inamdar
published in: Journal of Combinatorial Theory. Series A
publication date: 2003-03-26T00:00:00Z
review text: In the very nice paper under review the authors determine the words of minimum weight in the code of the incidence system of \(s\)- versus \(t\)-flats in a finite projective space \(\text{PG}(n,q)\). For \(0\leq s<t<n\), let \(\Delta_{s,t}(n,q)\) denote the incidence system whose points and blocks are the \(s\)- and \(t\)-flats in \(\text{PG}(n,q)\), and the incidence is the set-theoretic inclusion. Let \(C_{s,t}(n,q)\) denote the \(p\)-ary code of \(\Delta_{s,t}(n,q)\). The main result states that the minimum weight words of \(C_{s,t}(n,q)\) are the scalar multiples of the blocks of \(\Delta_{s,t}(n,q)\).
Mathematics Subject Classification ID: 94B25
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51A45
zbMATH DE Number: 1888405
zbMATH Keywords: projective geometric codes
zbMATH Keywords: minimum weight words
reviewed by: Antonio Cossidente
MaRDI profile type: Publication
full work available at URL: jcta.2002.3265
OpenAlex ID: W2076734441
cites work: Q4004114
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DOI: 10.1006/JCTA.2002.3265
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description: scientific article; zbMATH DE number 1888405