### André embeddings of affine planes

(2010) Contemporary Mathematics. 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.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-1199279

- author
- Joseph Thas UGent and Hendrik Van Maldeghem UGent
- organization
- alternative title
- Andre embeddings of affine planes
- year
- 2010
- 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
- Toronto, ON, Canada
- 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
- copyright statement
*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}, location = {Toronto, ON, Canada}, 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.