This work investigates the structure of rank-metric codes in connection with concepts from
finite geometry, most notably the q-analogues of projective systems and blocking sets. We …

A strong blocking set in a finite projective space is a set of points that intersects each
hyperplane in a spanning set. We provide a new graph theoretic construction of such sets …

In this paper, we first study in detail the relationship between minimal linear codes and
cutting blocking sets, recently introduced by Bonini and Borello, and then completely …

Minimal linear codes are in one-to-one correspondence with special types of blocking sets
of projective spaces over a finite field, which are called strong or cutting blocking sets …

We develop three approaches of combinatorial flavor to study the structure of minimal codes
and cutting blocking sets in finite geometry, each of which has a particular application. The …

We prove new upper bounds on the smallest size of affine blocking sets, that is, sets of
points in a finite affine space that intersect every affine subspace of a fixed codimension. We …

Strong blocking sets, introduced first in 2011 in connection with saturating sets, have
recently gained a lot of attention due to their correspondence with minimal codes. In this …

Let PG⁡(r, q) be the r-dimensional projective space over the finite field GF⁡(q). A set 𝒳 of
points of PG⁡(r, q) is a cutting blocking set if for each hyperplane Π of PG⁡(r, q) the set Π∩ …

Let k≤ n be two positive integers and qa prime power. The basic question in minimal linear
codes is to determine if there exists an [n, k] q minimal linear code. The first objective of this …

The main purpose of this paper is to further study the structure, parameters and
constructions of the recently introduced minimal codes in the sum‐rank metric. These …