5 papers · 1 filter
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…