Corrado Zanella

activity

20122025

most citedVertex properties of maximum scattered linear sets of

PG (1, q^{n})

26 citations · 103 across the 23 of their papers we have counts for

collaborators

26 papers

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.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.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★ 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.CO2019★ 6 cited

A new family of maximum scattered linear sets in $PG (1, q^{6})$

Daniele Bartoli, Corrado Zanella, Ferdinando Zullo

We generalize the example of linear set presented by the last two authors in "Vertex properties of maximum scattered linear sets of $PG (1, q^{n})$ " (2019) to a more general f…

math.CO2019★ 1 cited

A condition for scattered linearized polynomials involving Dickson matrices

Corrado Zanella

A linearized polynomial over $F_{q^{n}}$ is called scattered when for any $t, x \in F_{q^{n}}$ , the condition $x f (t) - t f (x) = 0$ holds if and only if $x$ and $t$ are $\mathbb…

math.CO2019★ 26 cited

Vertex properties of maximum scattered linear sets of $PG (1, q^{n})$

Corrado Zanella, Ferdinando Zullo

In this paper we investigate the geometric properties of the configuration consisting of a $k$ -subspace $Γ$ and a canonical subgeometry $Σ$ in $PG (n - 1, q^{n})$ , with $Γ\capΣ=…

math.CO2019

A class of linear sets in PG(1,q^5)

Maria Montanucci, Corrado Zanella

The maximum scattered linear sets in $P G (1, q^{n})$ have been completely classified for $n \leq 4$ by Csajbók-Zanella and Lavrauw-Van de Voorde. Here a wide class of linear sets in $PG…

math.CO2017

A new family of MRD-codes

Bence Csajbók, Giuseppe Marino, Olga Polverino +1

We introduce a family of linear sets of $PG (1, q^{2 n})$ arising from maximum scattered linear sets of pseudoregulus type of $PG (3, q^{n})$ . For $n = 3, 4$ and for cert…

math.CO2017★ 2 cited

Maximum scattered $F_{q}$ -linear sets of $PG (1, q^{4})$

Bence Csajbók, Corrado Zanella

There are two known families of maximum scattered $F_{q}$ -linear sets in $P G (1, q^{t})$ : the linear sets of pseudoregulus type and for $t \geq 4$ the scattered linear sets found…

math.CO2016

Linear sets in the projective line over the endomorphism ring of a finite field

Hans Havlicek, Corrado Zanella

Let $PG (1, E)$ be the projective line over the endomorphism ring $E = E n d_{q} (F_{q^{t}})$ of the $F_{q}$ -vector space $F_{q^{t}}$ . As is well known there…

math.CO2015★ 2 cited

On scattered linear sets of pseudoregulus type in $PG (1, q^{t})$

Bence Csajbók, Corrado Zanella

Scattered linear sets of pseudoregulus type in $PG (1, q^{t})$ have been defined and investigated in [G. Lunardon, G. Marino, O. Polverino, R. Trombetti: Maximum scattered lin…

math.CO2015★ 2 cited

On the equivalence of linear sets

Bence Csajbók, Corrado Zanella

Let $L$ be a linear set of pseudoregulus type in a line $ℓ$ in $Σ^{*} = PG (t - 1, q^{t})$ , $t = 5$ or $t > 6$ . We provide examples of $q$ -order canonical subgeometries $Σ_1,\, Σ_2 \…

math.CO2014

Subspaces intersecting each element of a regulus in one point, André-Bruck-Bose representation and clubs

Michel Lavrauw, Corrado Zanella

In this paper results are proved with applications to the orbits of $(n - 1)$ -dimensional subspaces disjoint from a regulus $\cR$ of $(n - 1)$ -subspaces in $\PG(2n-1,q)$, with respect…

math.CO2014★ 2 cited

Subgeometries and linear sets on a projective line

Michel Lavrauw, Corrado Zanella

We define the splash of a subgeometry on a projective line, extending the definition of \cite{BaJa13} to general dimension and prove that a splash is always a linear set. We also p…

math.CO2013

Geometry of the inversion in a finite field and partitions of $PG (2^{k} - 1, q)$ in normal rational curves

Michel Lavrauw, Corrado Zanella

Let $L = F_{q^{n}}$ be a finite field and let $F = F_{q}$ be a subfield of $L$ . Consider $L$ as a vector space over $F$ and the associated projective space that is isomorph…

math.AG2013★ 4 cited

Incidence and Combinatorial Properties of Linear Complexes

Hans Havlicek, Corrado Zanella

In this paper a generalisation of the notion of polarity is exhibited which allows to completely describe, in an incidence-geometric way, the linear complexes of $h$ -subspaces. A g…

math.CO2013

Blocking sets in chain geometries

Andrea Blunck, Hans Havlicek, Corrado Zanella

In this paper we give some basic results on blocking sets on minimum size for a finite chain geometry.

math.CO2013★ 3 cited

Divisible designs from twisted dual numbers

Andrea Blunck, Hans Havlicek, Corrado Zanella

The generalized chain geometry over the local ring $K (ε; σ)$ of twisted dual numbers, where $K$ is a finite field, is interpreted as a divisible design obtained from an imprimitive…

math.CO2013★ 5 cited

Lifting of divisible designs

Andrea Blunck, Hans Havlicek, Corrado Zanella

The aim of this paper is to present a construction of $t$ -divisible designs for $t > 3$ , because such divisible designs seem to be missing in the literature. To this end, tools such…

math.AG2013★ 3 cited

On automorphisms of flag spaces

Hans Havlicek, Klaus List, Corrado Zanella

We show that the automorphisms of the flag space associated with a 3-dimensional projective space can be characterized as bijections preserving a certain binary relation on the set…

math.AG2013★ 9 cited

Veronese Varieties over Fields with non-zero Characteristic: A Survey

Hans Havlicek

In the present survey we collect some recent results on nuclei of Veronese varieties and invariant subspaces of normal rational curves. We must assume, however, that the ground fie…

math.AG2013★ 9 cited

On embedded products of Grassmannians

Hans Havlicek, Corrado Zanella

Let $Γ^{'}$ and $Γ$ be two Grassmannians. The standard embedding $ϕ : Γ^{'} \times Γ \to P ˉ$ is obtained by combining the Plücker and Segre embeddings. Given a further embedding $η: Γ'\t…

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

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

Partially scattered linearized polynomials and rank metric codes

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

A new family of maximum scattered linear sets in PG(1,q6)

A condition for scattered linearized polynomials involving Dickson matrices

Vertex properties of maximum scattered linear sets of PG(1,qn)

A class of linear sets in PG(1,q^5)

A new family of MRD-codes

Maximum scattered Fq​-linear sets of PG(1,q4)

Linear sets in the projective line over the endomorphism ring of a finite field

On scattered linear sets of pseudoregulus type in PG(1,qt)

On the equivalence of linear sets

Subspaces intersecting each element of a regulus in one point, André-Bruck-Bose representation and clubs

Subgeometries and linear sets on a projective line

Geometry of the inversion in a finite field and partitions of PG(2k−1,q) in normal rational curves

Incidence and Combinatorial Properties of Linear Complexes

Blocking sets in chain geometries

Divisible designs from twisted dual numbers

Lifting of divisible designs

On automorphisms of flag spaces

Veronese Varieties over Fields with non-zero Characteristic: A Survey

On embedded products of Grassmannians

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

A new family of maximum scattered linear sets in $PG (1, q^{6})$

Vertex properties of maximum scattered linear sets of $PG (1, q^{n})$

Maximum scattered $F_{q}$ -linear sets of $PG (1, q^{4})$

On scattered linear sets of pseudoregulus type in $PG (1, q^{t})$

Geometry of the inversion in a finite field and partitions of $PG (2^{k} - 1, q)$ in normal rational curves