This article updates the authors' 1998 survey [134] on the same theme that was written for
the Bose Memorial Conference (Colorado, June 7–11, 1995). That article contained the …

In this paper linear sets of finite projective spaces are studied and the “dual” of a linear set is
introduced. Also, some applications of the theory of linear sets are investigated: blocking …

Based on the simple and well understood concept of subfields in a finite field, the technique
called 'field reduction'has proved to be a very useful and powerful tool in finite geometry. In …

A subspace of matrices in can be naturally embedded as a subspace of matrices in with the
property that the rank of any of its matrix is a multiple of. It is quite natural to ask whether or …

We prove that a small minimal blocking set of PG (2, q) is “very close” to be a linear blocking
set over some subfield GF (pe)< GF (q). This implies that (i) a similar result holds in PG (n, q) …

In this paper we collect results on the possible sizes of k-blocking sets. Since 5 previous
surveys focused mainly on blocking sets in the plane, we concentrate our 6 attention on …

In 1970 Rédei and Megyesi proved that a set of p points in AG (2, p), p prime, is a line, or it
determines at least p+ 3 2 directions. In'81 Lovász and Schrijver characterized the case of …

We show that small blocking sets in PG (n, q) with respect to hyperplanes intersect every
hyperplane in 1 modulo p points, where q= ph. The result is then extended to blocking sets …

This one is not intended to be an introductory textbook about finite geometries, finite fields
nor polynomials. There are very good books of these kinds available, eg Ball-Weiner [23] for …

Some improved bounds on the number of directions not determined by a point set in the
affine space AG (k, q) are presented. More precisely, if there are more than pe (q− 1) …