G. Longobardi

activity

20192026

most citedLinear sets and MRD-codes arising from a class of scattered linearized polynomials

25 citations · 31 across the 18 of their papers we have counts for

collaborators

22 papers

math.CO2026

Near-uniform $q$ -matroids

Giovanni Longobardi, Rocco Trombetti, Lei Xu

We study the $q$ -matroids associated with nondegenerate $\F_{q^m}$-linear near-MRD codes, which we call near-uniform $q$ -matroids. Using the correspondence between rank-metric code…

math.CO2026

The classification of maximum scattered linear sets of $PG (1, q^{5})$

Giovanni Longobardi, Valentina Pepe

We classify the maximum scattered $F_{q}$ -linear sets of $PG (1, q^{5})$ , proving that every such set is of pseudoregulus type or of Lunardon-Polverino type. Building o…

math.CO2026

q-Polymatroids associated with restricted rank-metric codes

Eimear Byrne, Giovanni Longobardi, and Rocco Trombetti

In this article, we study polymatroids that are representable by means of linear restricted rank-metric codes, namely, by subspaces of the space of alternating, symmetric, or Hermi…

math.CO2026

Generalizing a family of scattered quadrinomials in $F_{q^{2 t}} [X]$

Alessandro Giannoni, Giovanni Giuseppe Grimaldi, Giovanni Longobardi +1

In recent years, several efforts have focused on identifying new families of scattered polynomials. Currently, only three families in $F_{q^{n}} [X]$ are known to exist for i…

math.CO2025

A lower bound on the minimum weight of some geometric codes

Bence Csajbók, Giovanni Longobardi, Giuseppe Marino +1

The $p$ -ary code associated with the incidence structure of points and $t$ -spaces in a projective space $PG (m, q)$ , where $q = p^{h}$ , is the $F_{p}$ -subspace generated…

math.CO2025

Towards the classification of maximum scattered linear sets of $PG (1, q^{5})$

Stefano Lia, Giovanni Longobardi, Corrado Zanella

Every maximum scattered linear set in $PG (1, q^{5})$ is the projection of an $F_{q}$ -subgeometry $Σ$ of $PG (4, q^{5})$ from a plane $Γ$ external to the secant va…

math.CO2025

Minimal codes from hypersurfaces in even characteristic

Angela Aguglia, Luca Giuzzi, Giovanni Longobardi +1

The setting of projective systems can be used to study the parameters of a projective linear code $C$ . This can be done by considering the intersections of the point set…

math.HO2024

Scattered polynomials: an overview on their properties, connections and applications

Giovanni Longobardi

The aim of this survey is to outline the state of the art in research on a class of linearized polynomials with coefficients over finite fields, known as scattered polynomials. The…

math.CO2024

A geometric characterization of known maximum scattered linear sets of $PG (1, q^{n})$

Giovanni Giuseppe Grimaldi, Somi Gupta, Giovanni Longobardi +1

An $F_{q}$ - linear set $L = L_{U}$ of $Λ = PG (V, F_{q^{n}}) ≅ PG (r - 1, q^{n})$ is a set of points defined by non-zero vectors of an $F_{q}$ -subspac…

math.CO2023

Scattered trinomials of $F_{q^{6}} [X]$ in even characteristic

Daniele Bartoli, Giovanni Longobardi, Giuseppe Marino +1

In recent years, several families of scattered polynomials have been investigated in the literature. However, most of them only exist in odd characteristic. In [B. Csajbók, G. Mari…

cs.IT2023

Short rank-metric codes and scattered subspaces

Stefano Lia, Giovanni Longobardi, Giuseppe Marino +1

By exploiting the connection between scattered $F_{q}$ -subspaces of $F_{q^{m}}^{3}$ and minimal non degenerate $3$ -dimensional rank metric codes of $\mathbb{F}_{q^m}^{n…

cs.IT2023

Non-linear MRD codes from cones over exterior sets

Nicola Durante, Giovanni Giuseppe Grimaldi, Giovanni Longobardi

By using the notion of $d$ -embedding $Γ$ of a (canonical) subgeometry $Σ$ and of exterior set with respect to the $h$ -secant variety $Ω_{h} (A)$ of a subset $A$ ,…

cs.IT2022

On the equivalence issue of a class of $2$ -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 $2$ -dimensional $F_{q^{2 t}}$ -linear MRD…

math.CO2022

Scattered linear sets in a finite projective line and translation planes

Valentina Casarino, Giovanni Longobardi, Corrado Zanella

Lunardon and Polverino construct a translation plane starting from a scattered linear set of pseudoregulus type in $PG (1, q^{t})$ . In this paper a similar construction of a t…

math.CO2022

A standard form for scattered linearized polynomials and properties of the related translation planes

Giovanni Longobardi, Corrado Zanella

In this paper we present results concerning the stabilizer $G_{f}$ in $GL (2, q^{n})$ of the subspace $U_{f} = {(x, f (x)) : x \in F_{q^{n}} [x]}$ , $f (x)$ a scattered lineari…

math.CO2021

$(d, σ)$ -Veronese variety and some applications

Nicola Durante, Giovanni Longobardi, Valentina Pepe

Let $K$ be the Galois field $F_{q^{t}}$ of order $q^{t}, q = p^{e}, p$ a prime, $A = Aut (K)$ be the automorphism group of $K$ and $\boldsymbolσ=(…

math.CO2021

A large family of maximum scattered linear sets of $PG (1, q^{n})$ 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…

math.CO2020

Partially scattered linearized polynomials and rank metric codes

Giovanni Longobardi, Corrado Zanella

A linearized polynomial $f (x) \in F_{q^{n}} [x]$ is called scattered if for any $y, z \in F_{q^{n}}$ , the condition $z f (y) - y f (z) = 0$ implies that $y$ and $z$ are $\mathbb F_{q…

math.CO2020

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…

math.CO2020★ 25 cited

Linear sets and MRD-codes arising from a class of scattered linearized polynomials

Giovanni Longobardi, Corrado Zanella

A class of scattered linearized polynomials covering infinitely many field extensions is exhibited. More precisely, the $q$ -polynomial over $F_{q^{6}}$ , $q \equiv 1 (mod 4)$ d…

math.CO2020

Maximal sets of $k$ -spaces pairwise intersecting in at least a $(k - 2)$ -space

Jozefien D'haeseleer, Giovanni Longobardi, Ago-Erik Riet +1

In this paper, we analyze the structure of maximal sets of $k$ -dimensional spaces in $PG (n, q)$ pairwise intersecting in at least a $(k - 2)$ -dimensional space, for $3 \leq k…

math.CO2019★ 6 cited

Automorphism groups and new constructions of maximum additive rank metric codes with restrictions

G. Longobardi, G. Lunardon, R. Trombetti +1

Let $d, n \in Z^{+}$ such that $1 \leq d \leq n$ . A $d$ -code $C \subset F_{q}^{n \times n}$ is a subset of order $n$ square matrices with the property that f…

Near-uniform q-matroids

The classification of maximum scattered linear sets of PG(1,q5)

q-Polymatroids associated with restricted rank-metric codes

Generalizing a family of scattered quadrinomials in Fq2t​[X]

A lower bound on the minimum weight of some geometric codes

Towards the classification of maximum scattered linear sets of PG(1,q5)

Minimal codes from hypersurfaces in even characteristic

Scattered polynomials: an overview on their properties, connections and applications

A geometric characterization of known maximum scattered linear sets of PG(1,qn)

Scattered trinomials of Fq6​[X] in even characteristic

Short rank-metric codes and scattered subspaces

Non-linear MRD codes from cones over exterior sets

On the equivalence issue of a class of 2-dimensional linear Maximum Rank Distance codes

Scattered linear sets in a finite projective line and translation planes

A standard form for scattered linearized polynomials and properties of the related translation planes

(d,σ)-Veronese variety and some applications

A large family of maximum scattered linear sets of PG(1,qn) and their associated MRD codes

Partially scattered linearized polynomials and rank metric codes

On sets of subspaces with two intersection dimensions and a geometrical junta bound

Linear sets and MRD-codes arising from a class of scattered linearized polynomials

Maximal sets of k-spaces pairwise intersecting in at least a (k−2)-space

Automorphism groups and new constructions of maximum additive rank metric codes with restrictions

Near-uniform $q$ -matroids

The classification of maximum scattered linear sets of $PG (1, q^{5})$

Generalizing a family of scattered quadrinomials in $F_{q^{2 t}} [X]$

Towards the classification of maximum scattered linear sets of $PG (1, q^{5})$

A geometric characterization of known maximum scattered linear sets of $PG (1, q^{n})$

Scattered trinomials of $F_{q^{6}} [X]$ in even characteristic

On the equivalence issue of a class of $2$ -dimensional linear Maximum Rank Distance codes

$(d, σ)$ -Veronese variety and some applications

A large family of maximum scattered linear sets of $PG (1, q^{n})$ and their associated MRD codes

Maximal sets of $k$ -spaces pairwise intersecting in at least a $(k - 2)$ -space