Galois geometries and coding theory are two research areas which have been interacting
with each other for many decades. From the early examples linking linear MDS codes with …

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 …

Recently, a lower bound was established on the size of linear sets in projective spaces, that
intersect a hyperplane in a canonical subgeometry. There are several constructions showing …

Apart from being an interesting and exciting area in combinatorics with beautiful results,
finite projective spaces or Galois geometries have many applications to coding theory …

Linear sets generalise the concept of subgeometries in a projective space. They have many
applications in finite geometry. In this paper we address two problems for linear sets: the …

Finite Geometries stands out from recent textbooks about the subject of finite geometries by
having a broader scope. The authors thoroughly explain how the subject of finite geometries …

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 this paper, we first determine the minimum possible size of an F q-linear set of rank k in
PG (1, qn). We obtain this result by relating it to the number of directions determined by a …

An F q-linear blocking set B of π= PG (2, qn), q= ph, n> 2, can be obtained as the projection
of a canonical subgeometry Σ≃ PG (n, q) of Σ∗= PG (n, qn) to π from an (n− 3)-dimensional …