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Mathematics of Computation
Journal of the American Mathematical Society
ISSN 1088-6842(e) ISSN 0025-5718(p)
     

The eight dimensional ovoids over GF(5)

Author(s): C. Charnes; U. Dempwolff.
Journal: Math. Comp. 70 (2001), 853-861.
MSC (2000): Primary 51E15, 68R05, 05B25
Posted: February 23, 2000
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Abstract | References | Similar articles | Additional information

Abstract:

In this article we outline a computer assisted classification of the ovoids in an orthogonal space of the type $\Omega^{+}(8,5)$.


References:

1.
A. Blokhuis and G. E. Moorhouse, Some $p$-ranks related to orthogonal spaces, J. Alg. Combinatorics 4 (1995), 295-316. MR 96g:51011

2.
C. Charnes, Quadratic matrices and translation planes of order $5^2$, Coding Theory, Design Theory, Group Theory, Proceedings of the M. Hall Conference, eds. D. Jungnickel and S. A. Vanstone, Wiley, New York 1993, pp. 155-161. MR 94h:51016

3.
C. Charnes and U. Dempwolff, The translation planes of order 49 and their automorphism groups, Math. Comp. 67 (1998), 1207-1224. MR 98g:51007

4.
J. H. Conway, P. B. Kleidman and R. A. Wilson, New families of ovoids in $\Omega_8^{+}$, Geom. Ded. 26 (1988), 157-170. MR 89h:51014

5.
T. Czerwinski and D. Oakden, The translation planes of order twenty-five, J. Comb. Theory (A) 59 (1992), 193-217. MR 93c:51009

6.
T. Czerwinski, The collineation groups of the translation planes of order 25, Geom. Ded. 39 (1991), 125-137. MR 92i:51013

7.
U. Dempwolff, Translation planes of order 27, Designs, Codes and Crypt. 4 (1994), 105-121. MR 95a:51012

8.
U. Dempwolff and A. Reifart, The classification of the translation planes of order 16 1, Geom. Ded. 15 (1983), 137-153. MR 86d:51006

9.
A. Gunawardena, Classification of ovoids in $\Omega_8^+(4)$, submitted for publication, 1996.

10.
W. M. Kantor, Ovoids and translation planes, Can. J. Math. 34 (1982), 1195-1207. MR 84b:51019

11.
W. M. Kantor, Spreads, translation planes and Kerdock sets 1, SIAM J. Alg. Discr. Math. 3 (1982), 151-165. MR 83m:51013b

12.
G. E. Moorhouse, Ovoids from the $E_8$ root lattice, Geom. Ded. 46 (1993), 287-297. MR 94d:51011

13.
G. Mason and E. E. Shult, The Klein correspondence and the ubiquity of certain translation planes, Geom. Ded. 21 (1986), 29-50. MR 87g:51002

14.
R. Mathon and G. Royle, The translation planes of order 49, Designs, Codes and Crypt. 5 (1995), 57-72. MR 95j:51016
15.
M. Schönert et al., GAP Groups, Algorithms and Programming 3.4.4, Lehrstuhl D für Mathematik, RWTH Aachen, 1997.

16.
E. E. Shult, Nonexistence of ovoids in $\Omega_{10}^+(3)$, J. Comb. Theory (A) 51 (1989), 250-257. MR 90f:51015

17.
J. A. Thas, Ovoids and spreads of finite classical polar spaces, Geom. Ded. 10 (1981), 135-144. MR 82g:05031

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Additional Information:

C. Charnes
Affiliation: Department of Computer Science, University of Melbourne, Parkville, VIC 3052 Australia
Email: charnes@cs.mu.oz.au

U. Dempwolff
Affiliation: FB Mathematik Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany
Email: dempwolff@mathematik.uni-kl.de

DOI: 10.1090/S0025-5718-00-01191-1
PII: S 0025-5718(00)01191-1
Received by editor(s): January 2, 1998
Received by editor(s) in revised form: April 20, 1999
Posted: February 23, 2000
Copyright of article: Copyright 2000, American Mathematical Society


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