G. Marino

activity

20122026

most citedOn the maximum field of linearity of linear sets

3 citations · 4 across the 7 of their papers we have counts for

collaborators

8 papers

cs.IT2026

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 $C$ and every admissible order $t$ , the $t$ -th generaliz…

math.CO2026

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.…

math.CO2026

Segre Varieties and Desarguesian Spreads

Antonio Cossidente, Giuseppe Marino, Francesco Pavese +2

Let $PG (n - 1, q)$ denote the $(n - 1)$ -dimensional projective space over $F_{q}$ . We investigate the intersection of two Desarguesian $(h - 1)$ -spreads of $\mathrm{PG}(kh…

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.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…

math.CO2023★ 3 cited

On the maximum field of linearity of linear sets

Bence Csajbók, Giuseppe Marino, Valentina Pepe

Let $V$ denote an $r$ -dimensional $F_{q^{n}}$ -vector space. For an $m$ -dimensional $F_{q}$ -subspace $U$ of $V$ assume that $\dim_q \left(\langle {\bf v}\rangle_{\math…

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…

math.CO2012★ 1 cited

Maximum scattered linear sets of pseudoregulus type and the Segre Variety $S_{n, n}$

G. Lunardon, G. Marino, O. Polverino +1

In this paper we study a family of scattered $\F_q$--linear sets of rank $t n$ of the projective space $P G (2 n - 1, q^{t})$ ( $n \geq 1$ , $t \geq 3$ ), called of {\it pseudoregulus type}, ge…