J. De Beule
Abstract
Let Q(2n + 2; q) denote the non-singular parabolic quadric in the projective geometry PG(2n + 2; q). We describe the implementation in GAP of an algorithm to study the problem of the minimal number of points of a minimal blocking set, different from an ovoid, of Q(4; q), for q = 5; 7.
- A. Beutelspacher and U. Rosenbaum. Projective Geometry. Cambridge University Press, 1998.Google Scholar
- A. Blokhuis. On the size of a blocking set in PG(2; p). Combinatorica, 14(1):111--114, 1994.Google ScholarCross Ref
- A. Blokhuis, L. Storme, and T. Szönyi. Lacunary polynomials, multiple blocking sets and Baer subplanes. J. London Math. Soc. (2), 60(2):321--332, 1999.Google ScholarCross Ref
- A. A. Bruen. Baer subplanes and blocking sets. Bull. Amer. Math. Soc., 76:342--344, 1970.Google ScholarCross Ref
- F. Buekenhout and E. E. Shult. On the foundations of polar geometry. Geom. Dedicata, 3:155--170, 1974.Google ScholarCross Ref
- J. De Beule, P. Govaerts, and L. Storme. Projective Geometries, a share package for GAP. http://cage.ugent.be/~jdebeule/pgGoogle Scholar
- J. De Beule and L. Storme. The smallest minimal blocking sets of Q(6; q), q even. J. Combin. Des., 11(4):290--303, 2003.Google ScholarCross Ref
- J. De Beule and L. Storme. On the smallest minimal blocking sets of Q(2n; q), for q an odd prime. Discrete Math., Proceedings of the First Irsee Conference on Finite Geometry (Irsee, 2003), to appear.Google Scholar
- J. Dittmann, A. Behr, M. Stabenau, P. Schmitt, J. Schwenk, and J. Ueberberg. Combining digital Watermarks and collusion secure Fingerprints for digital Images. http://www.ipsi.fraunhofer.de/~dittmann/pdf/spie-dittmann.pdfGoogle Scholar
- J. Eisfeld, L. Storme, T. Szönyi, and P. Sziklai. Covers and blocking sets of classical generalized quadrangles. Discrete Math., 238(1--3):35--51, 2001. Proceedings of The Third International Shanghai Conference on Designs, Codes and Finite Geometries (Shanghai, China, May 14--18, 1999). Google ScholarDigital Library
- The GAP Group, GAP -- Groups, Algorithms, and Programming, Version 4.3; 2002. http://www.gap-system.orgGoogle Scholar
- J. W. P. Hirschfeld. Projective Geometries Over Finite Fields. The Clarendon Press, Oxford University Press, New York, second edition, 1998.Google Scholar
- J. W. P. Hirschfeld and J. A. Thas. General Galois Geometries. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications.Google Scholar
- F. J. MacWilliams and N. J. A. Sloane. The Theory of Error Correcting Codes. North-Holland, 1977.Google Scholar
- K. Metsch. Small point sets that meet all generators of W(2n+1; q). Des. Codes Cryptogr., to appear. Google ScholarDigital Library
- MOSIX. http://www.mosix.orgGoogle Scholar
- A. Pasini. Diagram Geometries. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1994.Google Scholar
- S. E. Payne and J. A. Thas. Finite Generalized Quadrangles. Pitman (Advanced Publishing Program), Boston, MA, 1984.Google Scholar
- J. A. Thas. Ovoids and spreads of finite classical polar spaces. Geom. Dedicata, 10(1--4):135--143, 1981.Google Scholar
- N. Thomas. Projective geometry. http://www.anth.org.uk/NCT/Google Scholar
Recommendations
On the smallest minimal blocking sets of Q(2n,q ), for q an odd prime
We characterize the smallest minimal blocking sets of Q(2n,q), q an odd prime, in terms of ovoids of Q(4,q) and Q(6,q). The proofs of these results are written for q=3,5,7 since for these values it was known that every ovoid of Q(4,q) is an elliptic ...
On the Largest Caps Contained in the Klein Quadric of PG(5, q), q Odd
This article studies the largest caps, of cardinality q3+q2+q+1, contained in the Klein quadric of PG(5, q), q odd. Presently, there are three examples of such caps known. They all are the intersection of the Klein quadric with a suitably chosen ...
A new family of tight sets in $${\mathcal {Q}}^{+}(5,q)$$Q+(5,q)
In this paper, we describe a new infinite family of $$\frac{q^{2}-1}{2}$$q2-12-tight sets in the hyperbolic quadrics $${\mathcal {Q}}^{+}(5,q)$$Q+(5,q), for $$q \equiv 5 \text{ or } 9 \,\hbox {mod}\,{12}$$q 5or9mod12. Under the Klein correspondence, ...
Comments