8 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…
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…
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…