44 citations · 57 across the 28 of their papers we have counts for
14 papers · 1 filter
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…
Delsarte duality on subspaces and applications to rank-metric codes and q-matroids
Martino Borello, Olga Polverino, Ferdinando Zullo
We study the interplay between the lattice of F_{q^m}-subspaces and the lattice of F_{q^m}-subspaces of an F_{q^m}-vector space. Introducing notions of weight and defect relative t…
Linear rank-metric intersecting codes
Daniele Bartoli, Martino Borello, Giuseppe Marino +1
In this paper we introduce and investigate rank-metric intersecting codes, a new class of linear codes in the rank-metric context, inspired by the well-studied notion of intersecti…
The geometry of covering codes in the sum-rank metric
Matteo Bonini, Martino Borello, Eimear Byrne
We introduce the concept of a sum-rank saturating system and outline its correspondence to a covering properties of a sum-rank metric code. We consider the problem of determining t…
The geometry of intersecting codes and applications to additive combinatorics and factorization theory
Martino Borello, Wolfgang Schmid, Martin Scotti
Intersecting codes are linear codes where every two nonzero codewords have non-trivially intersecting support. In this article we expand on the theory of this family of codes, by s…
Saturating linear sets of minimal rank
Daniele Bartoli, Martino Borello, Giuseppe Marino
Saturating sets are combinatorial objects in projective spaces over finite fields that have been intensively investigated in the last three decades. They are related to the so-call…
Geometric dual and sum-rank minimal codes
Martino Borello, Ferdinando Zullo
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 objects form a…
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…
Saturating systems and the rank covering radius
Matteo Bonini, Martino Borello, Eimear Byrne
We introduce the concept of a rank saturating system and outline its correspondence to a rank-metric code with a given covering radius. We consider the problem of finding the value…
Small Strong Blocking Sets by Concatenation
Daniele Bartoli, Martino Borello
Strong blocking sets and their counterparts, minimal codes, attracted lots of attention in the last years. Combining the concatenating construction of codes with a geometric insigh…
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…
The uncertainty principle over finite fields
Martino Borello, Patrick Solé
In this paper we study the uncertainty principle (UP) connecting a function over a finite field and its Mattson-Solomon polynomial, which is a kind of Fourier transform in positive…
On involutions in extremal self-dual codes and the dual distance of semi self-dual codes
Martino Borello, Gabriele Nebe
A classical result of Conway and Pless is that a natural projection of the fixed code of an automorphism of odd prime order of a self-dual binary linear code is self-dual. In this…