11 papers · 1 filter
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…
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…
Representability of the direct sum of uniform q-matroids
Gianira N. Alfarano, Relinde Jurrius, Alessandro Neri +1
There are many similarities between the theories of matroids and -matroids. However, when dealing with the direct sum of -matroids many differences arise. Most notably, it ha…
On the weight distribution of linear sets with complementary weights and related constructions
Geertrui Van de Voorde, Ferdinando Zullo
In this paper, we continue the study of linear sets with complementary weights. We find criteria to determine the set of points of any fixed weight and use this to present particul…