Linear point sets and Redei type k-blocking sets in PG(n, q)

In this paper, k-blocking sets in PG(n, q), being of Redei type, are investigated. A standard method to construct Redei type k'-blocking sets in PG(n, q) is to construct a cone having as base a Redei type k'-blocking set in a subspace of PG(n, q). But also other Redei 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 Redei type k-blocking set of PG(n, q = p(h)), p a prime power, which guarantees that the Redei type k-blocking set is a cone. This condition is sharp. We also show that small Redei type k-blocking sets are linear.