A geometric relationship between equivalent spreads
type: Item
instance of: scholarly article
title: A geometric relationship between equivalent spreads
zbMATH Open document ID: 1030.51001
DOI: 10.1023/A:1024707325988
author: Keith E. Mellinger
published in: Designs, Codes and Cryptography
publication date: 2003-09-07T00:00:00Z
review text: It is well known that a translation plane can be defined by a spread of a projective space \(P = PG(d, q)\) and vice versa. An \(n\)-spread of \(P = PG(d, q)\) is a set of \(n\)-dimensional subspaces partitioning the point set of \(P\). It may occur that an \(n\)-spread of \(PG(d, q)\) and an \(m\)-spread of \(PG(t, q)\) with \(n \neq m \) define the same translation plane. Two such spreads are called equivalent. In the article under review Mellinger provides a geometric algorithm to construct equivalent spreads. More precisely, if \(S_{m-1}\) is an \((m-1)\)-spread of \(PG(2m-1, q)\) defining a translation plane \(\pi\) of dimension \(n \neq m\) over its kernel, then the algorithm of Mellinger yields an \((n-1)\)-spread \(S_{n-1}\) of \(PG(2n-1, q)\) defining the same translation plane \(\pi\).
reviewed by: Johannes Ueberberg
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51E23
zbMATH DE Number: 1975927
zbMATH Keywords: equivalent spreads
MaRDI profile type: Publication
full work available at URL: a:1024707325988
OpenAlex ID: W1570547581
description: scientific article; zbMATH DE number 1975927