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 …

The equivalence problem of F q-linear sets of rank n of PG (1, qn) is investigated, also in
terms of the associated variety, projecting configurations, F q-linear blocking sets of Rédei …

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 …

Subspace codes have recently been used for error correction in random network coding. In
this work, we focus on one-orbit cyclic subspace codes. If S is an F_q-subspace of F_q^n …

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 …

An F q-linear set of rank k, k≤ h, on a projective line PG (1, qh), containing at least one point
of weight one, has size at least qk− 1+ 1 (see De Beule and Van De Voorde (2019)). The …

Clubs of rank are well-celebrated objects in finite geometries introduced by Fancsali and
Sziklai in 2006. After the connection with a special type of arc known as a KM-arc, they …

In this paper, we investigate the André/Bruck-Bose representation of certain F q-linear sets
contained in a line of PG (2, qt). We show that scattered F q-linear sets of rank 3 in PG (1, q …

Subspace codes have recently been used for error correction in random network coding. In
this work, we focus on one-orbit cyclic subspace codes. If $ S $ is an $\mathbb {F} _q …

The aim of this paper is to investigate the intersection problem between two linear sets in the
projective line over a finite field. In particular, we analyze the intersection between two clubs …