44 citations · 63 across the 24 of their papers we have counts for
17 papers · 1 filter
Additive codes arising from hypergraphs
Gianira N. Alfarano
We study the critical exponent of additive codes through an integer polymatroid associated with the code. We give a coding-theoretic proof of Whittle's Critical Theorem in this set…
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.…
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…
The polytope of all -rank functions
Gianira N. Alfarano, Sebastian Degen
A -rank function is a real-valued function defined on the subspace lattice that is non-negative, upper bounded by the dimension function, non-decreasing, and satisfies the submo…
The free product of -matroids
Gianira N. Alfarano, Eimear Byrne, Andrew Fulcher
We introduce the notion of the free product of -matroids, which is the -analogue of the free product of matroids. We study the properties of this noncommutative binary operat…
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 and alternating rank-metric codes
Aida Abiad, Gianira N. Alfarano, Alberto Ravagnani
In this note we apply a spectral method to the graph of alternating bilinear forms. In this way, we obtain upper bounds on the size of an alternating rank-metric code for given val…
Recursive properties of the characteristic polynomial of weighted lattices
Gianira N. Alfarano, Eimear Byrne
In this paper, we describe properties of the characteristic polynomial of a weighted lattice and show that it has a recursive description, which we use to obtain results on the cri…
Maximum Flag-Rank Distance Codes
Gianira N. Alfarano, Alessandro Neri, Ferdinando Zullo
In this paper we extend the study of linear spaces of upper triangular matrices endowed with the flag-rank metric. Such metric spaces are isometric to certain spaces of degenerate…
Outer Strong Blocking Sets
Gianira N. Alfarano, Martino Borello, Alessandro Neri
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 p…
The Cyclic Flats of a -Matroid
Gianira N. Alfarano, Eimear Byrne
In this paper we develop the theory of cyclic flats of -matroids. We show that the lattice of cyclic flats, together with their ranks, uniquely determines a -matroid and henc…
On Cyclic Matroids and their Applications
Gianira N. Alfarano, Karan Khathuria, Simran Tinani
A matroid is a combinatorial structure that captures and generalizes the algebraic concept of linear independence under a broader and more abstract framework. Matroids are closely…
Linear Cutting Blocking Sets and Minimal Codes in the Rank Metric
Gianira N. Alfarano, Martino Borello, Alessandro Neri +1
This work investigates the structure of rank-metric codes in connection with concepts from finite geometry, most notably the -analogues of projective systems and blocking sets.…
Three Combinatorial Perspectives on Minimal Codes
Gianira N. Alfarano, Martino Borello, Alessandro Neri +1
We develop three approaches of combinatorial flavour to study the structure of minimal codes and cutting blocking sets in finite geometry, each of which has a particular applicatio…