8 papers
A proof of the generalized packing-covering conjecture
Gianira N. Alfarano, Giuseppe Marino, Alessandro Neri +1
The generalized packing--covering conjecture of Elimelech, Firer and Schwartz asserts that, for every linear code and every admissible order , the -th generaliz…
On the Etzion-Silberstein conjecture for block Ferrers diagrams
Marco Calderini, Marta Messia, Alessandro Neri
Ferrers diagram rank-metric codes are rank-metric codes with prescribed support, and their dimension is bounded from above by the Etzion--Silberstein bound. In this paper, we study…
Combinatorial constructions of Schubert subspace codes
Gianira N. Alfarano, Alessandro Neri, Beatrice Toesca
We study Schubert subspace codes, which are constant-dimension subspace codes with prescribed intersection conditions with a fixed subspace. Our goal is to construct codes of maxim…
A geometric approach to generalized covering radii of linear codes
Gianira N. Alfarano, Giuseppe Marino, Alessandro Neri +1
Covering problems in coding theory are closely related to finite geometry through the interpretation of the columns of parity-check matrices as point sets in finite vector spaces.…
Rank-metric codes over arbitrary fields: Bounds and constructions
Alessandro Neri, Ferdinando Zullo
Rank-metric codes, defined as sets of matrices over a finite field with the rank distance, have gained significant attention due to their applications in network coding and connect…
Skew polynomial representations of matrix algebras and applications to coding theory
Alessandro Neri, Paolo Santonastaso
We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance b…
Representability of the direct sum of uniform q-matroids
Gianira N. Alfarano, Relinde Jurrius, Alessandro Neri +1
There are many similarities between the theories of matroids and -matroids. However, when dealing with the direct sum of -matroids many differences arise. Most notably, it ha…
Eigenvalue bounds for the distance- chromatic number of a graph and their application to Lee codes
Aida Abiad, Alessandro Neri, Luuk Reijnders
We derive eigenvalue bounds for the -distance chromatic number of a graph, which is a generalization of the classical chromatic number. We apply such bounds to hypercube graphs,…