Partial ovoids and partial spreads in hermitian polar spaces

Designs, Codes, and Cryptography

Volumn 47, Issue 1-3, 2008, Pages 21-34

  De Beule, J ^a   Klein, A ^a   Metsch, K ^b   Storme, L ^a  

^a GHENT UNIVERSITY   (Belgium)

^b JUSTUS LIEBIG UNIVERSITY   (Germany)

Author keywords

Hermitian variety; Partial ovoid; Partial spread; Polar space

Indexed keywords

COMPUTER SEARCHES; HERMITIAN; HERMITIAN VARIETY; LOWER BOUNDS; PARTIAL OVOID; PARTIAL SPREAD; POLAR SPACE; SYMPLECTIC; THEORETICAL ARGUMENTS; UPPER BOUNDS;

CONTROL THEORY;

EID: 64949088897     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10623-007-9047-8     Document Type: Article

References (19)

1. A Aguglia A Cossidente GL Ebert 2003 Complete spans on Hermitian varieties Des Codes Cryptogr 29 1-3 7 15
2. A Aguglia GL Ebert D Luyckx 2005 On partial ovoids of Hermitian surfaces Bull Belg Math Soc Simon Stevin 12 5 641 650
3. A Blokhuis GE Moorhouse 1995 Some p-ranks related to orthogonal spaces J Algebraic Comb 4 4 295 316
4. RC Bose RC Burton 1966 A characterization of flat spaces in a finite geometry and the uniqueness of the Hamming and the MacDonald codes J Comb Theory 1 96 104
5. AA Bruen 1980 Blocking sets and skew subspaces of projective space Can J Math 32 3 628 630
6. Cimráková M, De Winter S, Fack V, Storme L (2006) On the smallest maximal partial ovoids and spreads of the generalized quadrangles W(q) and Q(4,q). Eur J Comb, doi:10.1016/j.ejc.2006.11.001
7. 3 + 1. J Comb Theory Ser A, doi:10.1016/j.jcta. 2006.08.005
8. De Beule J, Klein A, Metsch K, Storme L (2007) Partial ovoids and partial spreads in symplectic and orthogonal polar spaces. Eur J comb (submitted)
9. RH Dye 1992 Maximal sets of nonpolar points of quadrics and symplectic polarities over GF(2) Geom Dedicata 44 3 281 293
10. GL Ebert JWP Hirschfeld 1999 Complete systems of lines on a Hermitian surface over a finite field Des Codes Cryptogr 17 1-3 253 268
11. P Govaerts L Storme H Van Maldeghem 2002 On a particular class of minihypers and its applications. III Applications. Eur J Comb 23 6 659 672
12. Hirschfeld JWP, Thas JA (1991) General Galois geometries. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, Oxford Science Publications, New York
13. A Klein K Metsch 2005 New results on covers and partial spreads of polar spaces Innov Incidence Geom 1 19 34
14. n ) (preprint)
15. 2) Innov Incidence Geom 3 1 12
16. Metsch K, Storme L. Maximal partial ovoids and maximal partial spreads in hermitian generalized quadrangles. J Comb Des, doi:10.1002/jcd.20146
17. Payne SE, Thas JA (1984) Finite generalized quadrangles, volume 110 of research notes in mathematics. Pitman (Advanced Publishing Program), Boston, MA
18. Thas JA (1992) Old and new results on spreads and ovoids of finite classical polar spaces. In: Proceedings of Combinatorics '90 (Gaeta, 1990). Annals of discrete mathematics, vol 52. North-Holland, Amsterdam, pp 529-544
19. Thas JA (2001) Ovoids, spreads and m-systems of finite classical polar spaces. In: Surveys in combinatorics, 2001 (Sussex). London mathematical society lecture note series, vol 288. Cambridge University Press, Cambridge, pp 241-267