### André embeddings of affine planes

Joseph Thas UGent and Hendrik Van Maldeghem UGent (2010) 523. p.123-131
abstract
An Andre embedding is a representation of a point-line geometry S with approximately s(2) points on a line in a planar space with approximately s points per line, but such that the lines of S are contained in planes of the planar space. An example is the Andre representation (also sometimes called the Bose-Bruck representation) of an affine translation plane of order q(2) (with kernel of order at least q) in 4-dimensional affine space AG(4, q), using a line spread at infinity. In this paper, we classify all Andre embeddings of affine planes of order q(2) in PG(4, q), q > 2, and obtain, besides the natural extension to PG(4, q) of the above example, two other related constructions. We also consider Andre embeddings of affine planes of order q(2) in PG(d, q), with d > 4 and q > 2.
author
organization
alternative title
Andre embeddings of affine planes
year
type
conference (proceedingsPaper)
publication status
published
subject
in
Contemporary Mathematics
editor
AA Bruen and DL Wehlau
volume
523
issue title
Error-correcting codes, finite geometries and cryptography
pages
123 - 131
publisher
American Mathematical Society
place of publication
Providence, RI, USA
conference name
Conference on Error-Control Codes, Information Theory and Applied Cryptography
conference location
conference start
2007-12-05
conference end
2007-12-06
Web of Science type
Proceedings Paper
Web of Science id
000283176500010
ISSN
0271-4132
ISBN
9780821849569
language
English
UGent publication?
yes
classification
P1
I have transferred the copyright for this publication to the publisher
id
1199279
handle
http://hdl.handle.net/1854/LU-1199279
date created
2011-03-30 13:06:29
date last changed
2017-01-02 09:52:26
```@inproceedings{1199279,
abstract     = {An Andre embedding is a representation of a point-line geometry S with approximately s(2) points on a line in a planar space with approximately s points per line, but such that the lines of S are contained in planes of the planar space. An example is the Andre representation (also sometimes called the Bose-Bruck representation) of an affine translation plane of order q(2) (with kernel of order at least q) in 4-dimensional affine space AG(4, q), using a line spread at infinity. In this paper, we classify all Andre embeddings of affine planes of order q(2) in PG(4, q), q {\textrangle} 2, and obtain, besides the natural extension to PG(4, q) of the above example, two other related constructions. We also consider Andre embeddings of affine planes of order q(2) in PG(d, q), with d {\textrangle} 4 and q {\textrangle} 2.},
author       = {Thas, Joseph and Van Maldeghem, Hendrik},
booktitle    = {Contemporary Mathematics},
editor       = {Bruen, AA and Wehlau, DL},
isbn         = {9780821849569},
issn         = {0271-4132},
language     = {eng},
pages        = {123--131},
publisher    = {American Mathematical Society},
title        = {Andr{\'e} embeddings of affine planes},
volume       = {523},
year         = {2010},
}

```
Chicago
Thas, Joseph, and Hendrik Van Maldeghem. 2010. “André Embeddings of Affine Planes.” In Contemporary Mathematics, ed. AA Bruen and DL Wehlau, 523:123–131. Providence, RI, USA: American Mathematical Society.
APA
Thas, J., & Van Maldeghem, H. (2010). André embeddings of affine planes. In A. Bruen & D. Wehlau (Eds.), Contemporary Mathematics (Vol. 523, pp. 123–131). Presented at the Conference on Error-Control Codes, Information Theory and Applied Cryptography, Providence, RI, USA: American Mathematical Society.
Vancouver
1.
Thas J, Van Maldeghem H. André embeddings of affine planes. In: Bruen A, Wehlau D, editors. Contemporary Mathematics. Providence, RI, USA: American Mathematical Society; 2010. p. 123–31.
MLA
Thas, Joseph, and Hendrik Van Maldeghem. “André Embeddings of Affine Planes.” Contemporary Mathematics. Ed. AA Bruen & DL Wehlau. Vol. 523. Providence, RI, USA: American Mathematical Society, 2010. 123–131. Print.