13 papers
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…
Minimal additive codes and additive strong blocking sets
Gianira N. Alfarano, Marine Le Meur
Additive codes over generalize linear codes by relaxing linearity over the alphabet while retaining linearity over the subfield . In this paper, we…
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.…
On perfect flag-rank metric codes
Gianira N. Alfarano, Usman Mushrraf, Ferdinando Zullo
Flag-rank-metric codes arise as a natural generalization of rank-metric codes in the context of network communication. While recent research has mainly focused on algebraic and str…
The geometry of rank-metric codes
Gianira N. Alfarano, Martino Borello, Alessandro Neri
In this paper, we develop a geometric framework for matrix rank-metric codes based on generator tensors and their slice spaces. To every nondegenerate matrix rank-metric code, we a…
Representability of -matroids via rank-metric codes
Gianira N. Alfarano, Sebastian Degen
Multilinear representability extends classical linear representability of matroids by assigning subspaces, rather than vectors, to ground elements. This notion is closely related t…