44 citations · 57 across the 28 of their papers we have counts for
40 papers
A -analogue of the rational normal curve and linearized Reed-Solomon codes
Valentina Astore, Martino Borello, Alain Couvreur +1
The relationship between linear codes in the Hamming metric and projective algebraic varieties has led to deep interactions between coding theory and algebraic geometry, with class…
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…
On the existence of linear rank-metric intersecting codes
Martino Borello, Olga Polverino, Ferdinando Zullo
Intersecting codes are a classical object in coding theory whose rank-metric analogue has recently been introduced. Although the definition formally parallels the Hamming-metric ca…
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…
A geometric invariant of linear rank-metric codes
Valentina Astore, Martino Borello, Marco Calderini +1
Rank-metric codes have been a central topic in coding theory due to their theoretical and practical significance, with applications in network coding, distributed storage, crisscro…
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…
Dihedral Quantum Codes
Nadja Willenborg, Martino Borello, Anna-Lena Horlemann +1
We establish dihedral quantum codes of short block length, a class of CSS codes obtained by the lifted product construction. We present the code construction and give a formula for…
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…
Twisted skew -codes
Angelot Behajaina, Martino Borello, Javier de la Cruz +1
In this paper we investigate left ideals as codes in twisted skew group rings. The considered rings, which are often algebras over a finite field, allows us to detect many of the w…
Left ideal LRPC codes and a ROLLO-type cryptosystem based on group algebras
Martino Borello, Paolo Santonastaso, Ferdinando Zullo
In this paper we introduce left ideal low-rank parity-check codes by using group algebras and we finally use them to extend ROLLO-I KEM.
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…
On ideals in group algebras: an uncertainty principle and the Schur product
Martino Borello, Wolfgang Willems, Giovanni Zini
In this paper we investigate some properties of ideals in group algebras of finite groups over fields. First, we highlight an important link between their dimension, their minimal…
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…
Dihedral codes with prescribed minimum distance
Martino Borello, Abdelillah Jamous
Dihedral codes, particular cases of quasi-cyclic codes, have a nice algebraic structure which allows to store them efficiently. In this paper, we investigate it and prove some lowe…
A geometric characterization of minimal codes and their asymptotic performance
Gianira Nicoletta Alfarano, Martino Borello, Alessandro Neri
In this paper, we give a geometric characterization of minimal linear codes. In particular, we relate minimal linear codes to cutting blocking sets, introduced in a recent paper by…
On the algebraic structure of quasi group codes
Martino Borello, Wolfgang Willems
In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, a…
A Note on Linear Complementary Pairs of Group Codes
Martino Borello, Javier de la Cruz, Wolfgang Willems
We give a short and elementary proof of the fact that for a linear complementary pair , where and are -sided ideals in a group algebra, is uniquely determined…