G. Longobardi

activity

20192024

collaborators

5 papers

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.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

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

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…