100 citations · 209 across the 19 of their papers we have counts for
23 papers
Near-uniform -matroids
Giovanni Longobardi, Rocco Trombetti, Lei Xu
We study the -matroids associated with nondegenerate $\F_{q^m}$-linear near-MRD codes, which we call near-uniform -matroids. Using the correspondence between rank-metric code…
A proof of the generalized packing-covering conjecture
Gianira N. Alfarano, Giuseppe Marino, Alessandro Neri +1
The generalized packing--covering conjecture of Elimelech, Firer and Schwartz asserts that, for every linear code and every admissible order , the -th generaliz…
A geometric approach to generalized covering radii of linear codes
Gianira N. Alfarano, Giuseppe Marino, Alessandro Neri +1
Covering problems in coding theory are closely related to finite geometry through the interpretation of the columns of parity-check matrices as point sets in finite vector spaces.…
A lower bound on the minimum weight of some geometric codes
Bence Csajbók, Giovanni Longobardi, Giuseppe Marino +1
The -ary code associated with the incidence structure of points and -spaces in a projective space , where , is the -subspace generated…
A geometric characterization of known maximum scattered linear sets of
Giovanni Giuseppe Grimaldi, Somi Gupta, Giovanni Longobardi +1
An - linear set of is a set of points defined by non-zero vectors of an -subspac…
Short rank-metric codes and scattered subspaces
Stefano Lia, Giovanni Longobardi, Giuseppe Marino +1
By exploiting the connection between scattered -subspaces of and minimal non degenerate -dimensional rank metric codes of $\mathbb{F}_{q^m}^{n…
On the equivalence issue of a class of -dimensional linear Maximum Rank Distance codes
S. Gupta, G. Longobardi, R. Trombetti
In [A. Neri, P. Santonastaso, F. Zullo. Extending two families of maximum rank distance codes], the authors extended the family of -dimensional -linear MRD…
Evasive subspaces, generalized rank weights and near MRD codes
Giuseppe Marino, Alessandro Neri, Rocco Trombetti
We revisit and extend the connections between -linear rank-metric codes and evasive -subspaces of . We give a unifying framework…
A large family of maximum scattered linear sets of and their associated MRD codes
Giovanni Longobardi, Giuseppe Marino, Rocco Trombetti +1
The concept of linear set in projective spaces over finite fields was introduced by Lunardon in 1999 and it plays central roles in the study of blocking sets, semifields, rank-dist…
On sets of subspaces with two intersection dimensions and a geometrical junta bound
Giovanni Longobardi, Leo Storme, Rocco Trombetti
In this article, constant dimension subspace codes whose codewords have subspace distance in a prescribed set of integers, are considered. The easiest example of such an object is…
Evasive subspaces
Daniele Bartoli, Bence Csajbók, Giuseppe Marino +1
Let denote an -dimensional vector space over , the finite field of elements. Then is also an -dimension vector space over . An…
On maximum additive Hermitian rank-metric codes
Rocco Trombetti, Ferdinando Zullo
Inspired by the work of Zhou "On equivalence of maximum additive symmetric rank-distance codes" (2020) based on the paper of Schmidt "Symmetric bilinear forms over finite fields wi…
Automorphism groups and new constructions of maximum additive rank metric codes with restrictions
G. Longobardi, G. Lunardon, R. Trombetti +1
Let such that . A -code is a subset of order square matrices with the property that f…
A new family of MRD codes in with right and middle nuclei
Rocco Trombetti, Yue Zhou
In this paper, we present a new family of maximum rank distance (MRD for short) codes in of minimum distance . In particular, when $d=…
Nuclei and automorphism groups of generalized twisted Gabidulin codes
Rocco Trombetti, Yue Zhou
Generalized twisted Gabidulin codes are one of the few known families of maximum rank matrix codes over finite fields. As a subset of m by n matrices, when m=n, the automorphism gr…
On kernels and nuclei of rank metric codes
Guglielmo Lunardon, Rocco Trombetti, Yue Zhou
For each rank metric code , we associate a translation structure, the kernel of which is shown to be invariant with respect to the equi…
Hyperovals in Knuth's binary semifield planes
Nicola Durante, Rocco Trombetti, Yue Zhou
In each of the three projective planes coordinatised by the Knuth's binary semifield of order and two of its Knuth derivatives, we exhibit a new family of infi…
On the 2-ranks of a class of unitals
Rocco Trombetti, Yue Zhou
Let be a unital defined in a shift plane of odd order , which are constructed recently by the authors. In particular, when the shift plane is desarguesian, is a sp…
Unitals in shift planes of odd order
Rocco Trombetti, Yue Zhou
A finite shift plane can be equivalently defined via abelian relative difference sets as well as planar functions. In this paper, we present a generic way to construct unitals in f…
Generalized Twisted Gabidulin Codes
Guglielmo Lunardon, Rocco Trombetti, Yue Zhou
Let be a set of by matrices over such that the rank of is at least for all distinct . Suppose that …
The isotopism problem of a class of 6-dimensional rank 2 semifields and its solution
Michel Lavrauw, Giuseppe Marino, Olga Polverino +1
In [U. Dempwolff: \textit{More Translation Planes and Semifields from Dembowski-Ostrom Polynomials}, Designs, Codes, Cryptogr. \textbf{68} (1-3) (2013), 81--103] three classes of r…
Solution to an isotopism question concerning rank 2 semifields
Michel Lavrauw, Giuseppe Marino, Olga Polverino +1
In [U. Dempwolff: More Translation Planes and Semifields from Dembowski-Ostrom Polynomials, Designs, Codes, Cryptogr. \textbf{68} (1-3) (2013), 81-103], the author gives a construc…
Maximum scattered linear sets of pseudoregulus type and the Segre Variety
G. Lunardon, G. Marino, O. Polverino +1
In this paper we study a family of scattered $\F_q$--linear sets of rank of the projective space (, ), called of {\it pseudoregulus type}, ge…