TY - JOUR UR - http://lib.ugent.be/catalog/pug01:513745 ID - pug01:513745 LA - eng TI - A hemisystem of a nonclassical generalised quadrangle PY - 2009 JO - (2009) DESIGNS CODES AND CRYPTOGRAPHY SN - 0925-1022 PB - 2009 AU - Bamberg, John AU - De Clerck, Frank UGent 801000311366 AU - Durante, Nicola AB - 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. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 513745 | ||
005 | 20180813143408.0 | ||
008 | 090303s2009------------------------eng-- | ||
022 | a 0925-1022 | ||
024 | a 000263300500005 2 wos | ||
024 | a 1854/LU-513745 2 handle | ||
024 | a 10.1007/s10623-008-9251-1 2 doi | ||
040 | a UGent | ||
245 | a A hemisystem of a nonclassical generalised quadrangle | ||
260 | c 2009 | ||
520 | a 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. | ||
598 | a A1 | ||
100 | a Bamberg, John u WE01 0 802000050051 | ||
700 | a De Clerck, Frank u UGent 0 801000311366 0 974053150353 | ||
700 | a Durante, Nicola | ||
650 | a Mathematics and Statistics | ||
653 | a Strongly regular graph | ||
653 | a Partial quadrangle | ||
653 | a Hemisystem | ||
653 | a Association scheme | ||
653 | a QUADRATIC CONE | ||
653 | a FLOCKS | ||
773 | t DESIGNS CODES AND CRYPTOGRAPHY g Designs Codes Cryptogr. 2009. 51 (2) p.157-165 q 51:2<157 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/513745/file/1008030 z [ugent] y Des._Codes_Cryptogr_2009_Bamberg-1.pdf | ||
920 | a article | ||
Z30 | x WE 1 WE01 | ||
922 | a UGENT-WE |
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