19 papers
Weak arcs and applications to the DNA-based storage access problem
Geertrui Van de Voorde, Ferdinando Zullo
Weak arcs are point sets in PG meeting every general hyperplane (those are the hyperplanes not going through one of the points given by the standard basis vectors) in at m…
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…
Symmetric Tensor Decompositions over Finite Fields
Giuseppe Cotardo, Ferdinando Zullo
We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified wit…
Semidefinite and linear programming bounds for sum-rank-metric codes and non-existence results
Aida Abiad, Antonina P. Khramova, Sven C. Polak +1
The sum-rank metric provides a unifying framework that generalizes both the celebrated Hamming and rank metrics, and has found applications in areas such as network coding, distrib…
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…
On the number of inequivalent linearized Reed-Solomon codes
Jonathan Mannaert, Marta Messia, Ferdinando Zullo
Linearized Reed-Solomon (LRS) codes form an important family of maximum sum-rank distance (MSRD) codes that generalize both Reed--Solomon codes and Gabidulin codes. In this paper w…