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Home > Vol 14, No 3 (2001)

L. Storme and P. Sziklai²

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In this paper, k-blocking sets in PG( n, q), being of Rédei type, are investigated. A standard method to construct Rédei type k-blocking sets in PG( n, q) is to construct a cone having as base a Rédei type k -blocking set in a subspace of PG( n, q). But also other Rédei type k-blocking sets in PG( n, q), which are not cones, exist. We give in this article a condition on the parameters of a Rédei type k-blocking set of PG( n, q = p ^h ), p a prime power, which guarantees that the Rédei type k-blocking set is a cone. This condition is sharp. We also show that small Rédei type k-blocking sets are linear.

1. A. Blokhuis, S. Ball, A. Brouwer, L. Storme, and T. Sz\Acute\Acute onyi, “On the number of slopes determined by a function on a finite field,” J. Combin. Theory, Ser. A 86 (1999), 187-196. STORME AND SZIKLAI
2. J.W.P. Hirschfeld, Projective Geometries over Finite Fields (Second Edition), Oxford University Press, Oxford, 1998.
3. G. Lunardon, “Linear k-blocking sets in PG(n, q),” Combinatorica, to appear.
4. L. Rédei, L\ddot uckenhafte Polynome \ddot uber endlichen K\ddot orpern, Birkh\ddot auser Verlag, Basel, 1970. (English translation: Lacunary Polynomials over Finite Fields, North-Holland, Amsterdam, 1973).