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A hemisystem of a nonclassical generalised quadrangle

John Bamberg UGent, Frank De Clerck and Nicola Durante (2009) DESIGNS CODES AND CRYPTOGRAPHY. 51(2). p.157-165
abstract
The concept of a hemisystem of a generalised quadrangle has its roots in the work of B. Segre, and this term is used here to denote a set of points H such that every line l meets H in half of the points of l. If one takes the point-line geometry on the points of the hemisystem, then one obtains a partial quadrangle and hence a strongly regular point graph. The only previously known hemisystems of generalised quadrangles of order (q, q (2)) were those of the elliptic quadric Q(-)(5, q) , q odd. We show in this paper that there exists a hemisystem of the Fisher-Thas-Walker-Kantor generalised quadrangle of order (5, 5(2)), which leads to a new partial quadrangle. Moreover, we can construct from our hemisystem the 3 . A (7)-hemisystem of Q-(5, 5), first constructed by Cossidente and Penttila.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Strongly regular graph, Partial quadrangle, Hemisystem, Association scheme, QUADRATIC CONE, FLOCKS
journal title
DESIGNS CODES AND CRYPTOGRAPHY
Designs Codes Cryptogr.
volume
51
issue
2
pages
157 - 165
Web of Science type
Article
Web of Science id
000263300500005
JCR category
MATHEMATICS, APPLIED
JCR impact factor
0.825 (2009)
JCR rank
102/202 (2009)
JCR quartile
3 (2009)
ISSN
0925-1022
DOI
10.1007/s10623-008-9251-1
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
513745
handle
http://hdl.handle.net/1854/LU-513745
date created
2009-03-03 16:14:11
date last changed
2016-12-19 15:40:40
@article{513745,
  abstract     = {The concept of a hemisystem of a generalised quadrangle has its roots in the work of B. Segre, and this term is used here to denote a set of points H such that every line l meets H in half of the points of l. If one takes the point-line geometry on the points of the hemisystem, then one obtains a partial quadrangle and hence a strongly regular point graph. The only previously known hemisystems of generalised quadrangles of order (q, q (2)) were those of the elliptic quadric Q(-)(5, q) , q odd. We show in this paper that there exists a hemisystem of the Fisher-Thas-Walker-Kantor generalised quadrangle of order (5, 5(2)), which leads to a new partial quadrangle. Moreover, we can construct from our hemisystem the 3 . A (7)-hemisystem of Q-(5, 5), first constructed by Cossidente and Penttila.},
  author       = {Bamberg, John and De Clerck, Frank and Durante, Nicola},
  issn         = {0925-1022},
  journal      = {DESIGNS CODES AND CRYPTOGRAPHY},
  keyword      = {Strongly regular graph,Partial quadrangle,Hemisystem,Association scheme,QUADRATIC CONE,FLOCKS},
  language     = {eng},
  number       = {2},
  pages        = {157--165},
  title        = {A hemisystem of a nonclassical generalised quadrangle},
  url          = {http://dx.doi.org/10.1007/s10623-008-9251-1},
  volume       = {51},
  year         = {2009},
}

Chicago
Bamberg, John, Frank De Clerck, and Nicola Durante. 2009. “A Hemisystem of a Nonclassical Generalised Quadrangle.” Designs Codes and Cryptography 51 (2): 157–165.
APA
Bamberg, J., De Clerck, F., & Durante, N. (2009). A hemisystem of a nonclassical generalised quadrangle. DESIGNS CODES AND CRYPTOGRAPHY, 51(2), 157–165.
Vancouver
1.
Bamberg J, De Clerck F, Durante N. A hemisystem of a nonclassical generalised quadrangle. DESIGNS CODES AND CRYPTOGRAPHY. 2009;51(2):157–65.
MLA
Bamberg, John, Frank De Clerck, and Nicola Durante. “A Hemisystem of a Nonclassical Generalised Quadrangle.” DESIGNS CODES AND CRYPTOGRAPHY 51.2 (2009): 157–165. Print.