Abstract
A family ℱ of ρ conics in PG(2,q) is called saturated if any line L⊂PG(2,q) is incident with at least one conic of the family. Then, if ρ<(q+1)/2, the ‘support’ of ℱ is a (k,n)-blocking set. It is shown that in this way one can get blocking sets whose character n is ‘small’ compared to q; it is also shown that ρ cannot be taken independent of q, but must necessarily increase as q does.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bartocci, U., ‘k-Insiemi densi in piani di Galois’, Bollettino U.M.I. VI (1983), 71–77.
Hirschfeld, J. W. P. Projective Geometries over Finite Fields, Clarendon Press, Oxford, 1979.
Menghini, M., ‘Una classe di blocking sets in PG(2,q)’, Atti Sem. Mat. Fis. Univ. Modena XXX (1981), 239–242.
Ughi, E., ‘Sul numero delle soluzioni di certi sistemi algebrici di congruenze in un campo di Galois’, Note di Matematica, Univ. di Lecce, 1986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ughi, E. On (k, n)-blocking sets which can be obtained as a union of conics. Geom Dedicata 26, 241–245 (1988). https://doi.org/10.1007/BF00183016
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00183016