The quintic Grassmannian \(\mathcal G_{1, 4, 2}\) in PG(9, 2)
type: Item
instance of: scholarly article
title: The quintic Grassmannian \(\mathcal G_{1, 4, 2}\) in PG(9, 2)
zbMATH Open document ID: 1062.51010
DOI: 10.1023/B:DESI.0000029236.10701.61
published in: Designs, Codes and Cryptography
publication date: 2004-08-16T00:00:00Z
review text: In this paper is studied the case \({\mathcal G}_{1,4,2}\subset \text{PG}(9,2)\) of the Grassmannian \({\mathcal G}_{1,4,2}\) of the lines of \(\text{PG}(4,2)\), for which a determined quintic \(Q\) has reduced degree \(5\). This structure is given explicitly by the authors in J. Comb. Theory, Ser. A 68, No.~1, 226--231 (1994; Zbl 0809.05022). The aim of this article is to study the associate \(X^\#\) of flats \(X\subset\text{PG}(9,2)\), as defined in terms of the completely polarized form \(Q^{++}\) of the quintic \(Q\). The associate \(X^\#\) is a generalization to \(\deg Q> 2\) of the orthogonal complement \(X^\perp\) in the case \(\deg Q= 2\).
reviewed by: Erhard Quaisser
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E14
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 2091529
zbMATH Keywords: Grassmannian \({\mathcal G}_{1,4,2}\)
zbMATH Keywords: particular spreads
zbMATH Keywords: \(\text{PG}(n,2)\)
zbMATH Keywords: quintic
zbMATH Keywords: associate of a flat
author: Ron Shaw
author: Neil Gordon
MaRDI profile type: Publication
full work available at URL: b:desi.0000029236.10701.61
OpenAlex ID: W2056523660
description: scientific article; zbMATH DE number 2091529