Linear Point Sets and Rédei Type k-blocking Sets in PG(n, q)

Abstract

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