12 citations · 19 across the 30 of their papers we have counts for
16 papers · 1 filter
Skew polynomial representations of matrix algebras and applications to coding theory
Alessandro Neri, Paolo Santonastaso
We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance b…
Adjoint and duality for rank-metric codes in a skew polynomial framework
José Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro +1
Skew polynomial rings provide a fundamental example of noncommutative principal ideal domains. Special quotients of these rings yield matrix algebras that play a central role in th…
Asymptotically optimal cyclic subspace codes
Chiara Castello, Paolo Santonastaso
Subspace codes, and in particular cyclic subspace codes, have gained significant attention in recent years due to their applications in error correction for random network coding.…
Invariants for sum-rank metric codes
Paolo Santonastaso, Ferdinando Zullo
The code equivalence problem is central in coding theory and cryptography. While classical invariants are effective for Hamming and rank metrics, the sum-rank metric, which unifies…
Completely decomposable rank-metric codes
Paolo Santonastaso
In this paper, we investigate completely decomposable rank-metric codes, i.e. rank-metric codes that are the direct sum of 1-dimensional maximum rank distance codes. We study the w…
Using multi-orbit cyclic subspace codes for constructing optical orthogonal codes
Ferruh Ozbudak, Paolo Santonastaso, Ferdinando Zullo
We present a new application of multi-orbit cyclic subspace codes to construct large optical orthogonal codes, with the aid of the multiplicative structure of finite fields extensi…
Two-weight rank-metric codes
Ferdinando Zullo, Olga Polverino, Paolo Santonastaso +1
Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting f…
On MSRD codes, h-designs and disjoint maximum scattered linear sets
Paolo Santonastaso, John Sheekey
In this paper we study geometric aspects of codes in the sum-rank metric. We establish the geometric description of generalised weights, and analyse the Delsarte and geometric dual…
Maximum weight codewords of a linear rank metric code
Olga Polverino, Paolo Santonastaso, Ferdinando Zullo
Let be an -linear non-degenerate rank metric code with dimension . In this paper we investigate the problem of determ…
Divisible linear rank metric codes
Olga Polverino, Paolo Santonastaso, John Sheekey +1
A subspace of matrices over can be naturally embedded as a subspace of matrices in with the property that the rank of an…
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.
On subspace designs
Paolo Santonastaso, Ferdinando Zullo
Guruswami and Xing introduced subspace designs in 2013 to give the first construction of positive rate rank metric codes list-decodable beyond half the distance. In this paper we p…
The geometry of one-weight codes in the sum-rank metric
Alessandro Neri, Paolo Santonastaso, Ferdinando Zullo
We provide a geometric characterization of -dimensional -linear sum-rank metric codes as tuples of -subspaces of . We then us…
Extending two families of maximum rank distance codes
Alessandro Neri, Paolo Santonastaso, Ferdinando Zullo
In this paper we provide a large family of rank-metric codes, which contains properly the codes recently found by Longobardi and Zanella (2021) and by Longobardi, Marino, Trombetti…
On the list decodability of rank-metric codes containing Gabidulin codes
Paolo Santonastaso, Ferdinando Zullo
Wachter-Zeh in [42], and later together with Raviv [31], proved that Gabidulin codes cannot be efficiently list decoded for any radius , providing that is large enough. Also…
On the list decodability of Rank Metric codes
Rocco Trombetti, Ferdinando Zullo
Let integers such that , let be a Delsarte-Gabidulin code. Wachter-Zeh proven that codes belonging…