Giovanni Giuseppe Grimaldi

activity

20232026

collaborators

9 papers

cs.IT2026

On the hull of linearized polynomial codes

Daniele Bartoli, Giovanni Giuseppe Grimaldi, Pantelimon Stănică

Motivated by entanglement-assisted quantum error-correcting codes, where the hull dimension determines the number of required pre-shared entangled pairs, we study hulls of two fami…

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.NT2025

On the Classification of Dillon's APN Hexanomials

Daniele Bartoli, Giovanni Giuseppe Grimaldi, Pantelimon Stanica

We systematically analyze a class of hexanomial functions over finite fields of characteristic $2$ proposed by Dillon (2006) as candidates for almost perfect nonlinear (APN) functi…

cs.CR2025

Homomorphic encryption schemes based on coding theory and polynomials

Giovanni Giuseppe Grimaldi

Homomorphic encryption is a powerful cryptographic tool that enables secure computations on the private data. It evaluates any function for any operation securely on the encrypted…

math.CO2025

Ovoids of $Q^{+} (7, q)$ of low-degree

Daniele Bartoli, Nicola Durante, Giovanni Giuseppe Grimaldi +1

Ovoids of the hyperbolic quadric $Q^{+} (7, q)$ of $PG (7, q)$ have been extensively studied over the past 40 years, partly due to their connections with other combinatorial obj…

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

On the classification of low degree ovoids of $Q^{+} (5, q)$

Daniele Bartoli, Nicola Durante, Giovanni Giuseppe Grimaldi

Ovoids of the Klein quadric $Q^{+} (5, q)$ of $PG (5, q)$ have been studied in the last 40 year, also because of their connection with spreads of $PG (3, q)$ and hence tr…

math.CO2023

On $m$ -ovoids of $Q^{+} (7, q)$ with $q$ odd

Sam Adriaensen, Jan De Beule, Giovanni Giuseppe Grimaldi +1

In this paper, we provide a construction of $(q + 1)$ -ovoids of the hyperbolic quadric $Q^{+} (7, q)$ , $q$ an odd prime power, by glueing $(q + 1) /2$ -ovoids of the elliptic quadric $Q^-(5,…

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 $A$ ,…

On the hull of linearized polynomial codes

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

On the Classification of Dillon's APN Hexanomials

Homomorphic encryption schemes based on coding theory and polynomials

Ovoids of Q+(7,q) of low-degree

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

On the classification of low degree ovoids of Q+(5,q)