F. Pavese

activity

20142025

most citedCombining subspace codes

41 citations · 45 across the 24 of their papers we have counts for

collaborators

32 papers

math.NT2025

Zeros of special polynomials and their impact on a class of APN functions

Daniele Bartoli, Marco Calderini, Giuseppe Marino +1

In 2021, Calderini et al. introduced a construction for APN functions on $F_{2^{2 m}}$ in bivariate form $$ f(x,y)=\big(xy,\, x^{2^r+1} + x^{2^{r+m/2}} y^{2^{m/2}} + bxy^{2…

math.CO2025

On line-parallelisms of PG(3, q)

Francesco Pavese, Paolo Santonastaso

Let $PG (3, q)$ denote the three-dimensional projective space over the finite field with $q$ elements. A line-spread of $PG (3, q)$ is a collection $S$ of…

math.CO2025

Strongly regular graphs from hyperbolic quadrics and their maximal cliques

Antonio Cossidente, Jan De Beule, Giuseppe Marino +2

Let $Q^{+} (2 n + 1, q)$ be a hyperbolic quadric of $\PG(2n+1,q)$. Fix a generator $Π$ of the quadric. Define $\cG_n$ as the graph with as vertex set the points of $Q^+(2n+1,q)\setminus Π…

math.CO2024

Affine vector space partitions and spreads of quadrics

Somi Gupta, Francesco Pavese

An affine spread is a set of subspaces of $AG (n, q)$ of the same dimension that partitions the points of $AG (n, q)$ . Equivalently, an {\em affine spread} is a set…

math.CO2023

An infinite family of $m$ -ovoids of the hyperbolic quadrics $Q^{+} (7, q)$

Francesco Pavese, Hanlin Zou

An infinite family of $(q^{2} + q + 1)$ -ovoids of $Q^{+} (7, q)$ , $q \equiv 1 (mod 3)$ , admitting the group $PGL (3, q)$ , is constructed. The main tool is the general theory…

math.CO2023

On 4-general sets in finite projective spaces

Francesco Pavese

A $4$ -general set in $PG (n, q)$ is a set of points of $PG (n, q)$ spanning the whole $PG (n, q)$ and such that no four of them are on a plane. Such a pointset is said…

math.CO2023

On the geometry of the Hermitian Veronese curve and its quasi-Hermitian surfaces

Michel Lavrauw, Stefano Lia, Francesco Pavese

The complete classification of the orbits on subspaces under the action of the projective stabiliser of (classical) algebraic varieties is a challenging task, and few classificatio…

math.CO2022★ 1 cited

The Geometry of $(t mod q)$ -arcs

Sascha Kurz, Ivan Landjev, Francesco Pavese +1

In this paper, we give a geometric construction of the three strong non-lifted $(3 mod 5)$ -arcs in $PG (3, 5)$ of respective sizes 128, 143, and 168, and construct an…

math.CO2022

On the geometry of a $(q + 1)$ -arc of $PG (3, q)$ , q even

Michela Ceria, Francesco Pavese

In $PG (3, q)$ , $q = 2^{n}$ , $n \geq 3$ , let $A = {(1, t, t^{2^{h}}, t^{2^{h} + 1}) ∣ t \in F_{q}} \cup {(0, 0, 0, 1)}$ , with $gcd (n, h) = 1$ , be a $(q + 1)$ -ar…

math.CO2022

The $m$ -ovoids of $W (5, 2)$

Michela Ceria, Francesco Pavese

In this paper we are concerned with $m$ -ovoids of the symplectic polar space $W (2 n + 1, q)$ , $q$ even. In particular we show the existence of an elliptic quadric of ${\rm PG}(…

math.CO2022

On large partial ovoids of symplectic and Hermitian polar spaces

Michela Ceria, Jan De Beule, Francesco Pavese +1

In this paper we provide constructive lower bounds on the sizes of the largest partial ovoids of the symplectic polar spaces $W (3, q)$ , $q$ odd square, $q \not\equiv 0 \pmod…

math.CO2021

A modular equality for $m$ -ovoids of elliptic quadrics

Alexander L. Gavrilyuk, Klaus Metsch, Francesco Pavese

An $m$ -ovoid of a finite polar space $P$ is a set $O$ of points such that every maximal subspace of $P$ contains exactly $m$ points of $O$ .…

math.CO2021

On near-MDS codes and caps

Michela Ceria, Antonio Cossidente, Giuseppe Marino +1

Several classes of near-MDS codes of $PG (3, q)$ are described. They are obtained either by considering the intersection of an elliptic quadric ovoid and a Suzuki-Tits ovoid of…

math.CO2021

Small complete caps in $PG (4 n + 1, q)$

Antonio Cossidente, Bence Csajbók, Giuseppe Marino +1

In this paper we prove the existence of a complete cap of $PG (4 n + 1, q)$ of size $2 (q^{2 n + 1} - 1) / (q - 1)$ , for each prime power $q > 2$ . It is obtained by projecting two disjoint V…

math.CO2021

A clique-free pseudorandom subgraph of the pseudo polarity graph

Sam Mattheus, Francesco Pavese

We provide a new family of $K_{k}$ -free pseudorandom graphs with edge density $Θ (n^{- 1/ (k - 1)})$ , matching a recent construction due to Bishnoi, Ihringer and Pepe. As in the former re…

math.CO2021

On regular systems of finite classical polar spaces

Antonio Cossidente, Giuseppe Marino, Francesco Pavese +1

Let $P$ be a finite classical polar space of rank $d$ . An $m$ -regular system with respect to $(k - 1)$ -dimensional projective spaces of $P$ , $1 \leq k \leq d - 1$ , is a set…

math.CO2020

Graphs cospectral with NU $(n + 1, q^{2})$ , $n \neq = 3$

Ferdinand Ihringer, Francesco Pavese, Valentino Smaldore

Let $H (n, q^{2})$ be a non-degenerate Hermitian variety of $P G (n, q^{2})$ , $n \geq 2$ . Let NU $(n + 1, q^{2})$ be the graph whose vertices are the points of $P G (n, q^{2}) ∖ H (n, q^{2})$ …

math.CO2020

On cutting blocking sets and their codes

Daniele Bartoli, Antonio Cossidente, Giuseppe Marino +1

Let PG $(r, q)$ be the $r$ -dimensional projective space over the finite field $GF (q)$ . A set $X$ of points of PG $(r, q)$ is a cutting blocking set if for each hyperplane…

math.CO2020

On symmetric and Hermitian rank distance codes

Antonio Cossidente, Giuseppe Marino, Francesco Pavese

Let $M$ denote the set $S_{n, q}$ of $n \times n$ symmetric matrices with entries in $GF (q)$ or the set $H_{n, q^{2}}$ of $n \times n$ Hermitian matrices who…

math.CO2019★ 41 cited

Combining subspace codes

Antonio Cossidente, Sascha Kurz, Giuseppe Marino +1

In the context of constant--dimension subspace codes, an important problem is to determine the largest possible size $A_{q} (n, d; k)$ of codes whose codewords are $k$ -subspaces of $\…

math.CO2019

On the PSU(4, 2)-invariant vertex-transitive strongly regular (216, 40, 4, 8) graph

Dean Crnković, Francesco Pavese, Andrea Švob

In 2018 the first, Rukavina and the third author constructed with the aid of a computer the first example of a strongly regular graph $Γ$ with parameters (216, 40, 4, 8) and proved…

math.CO2019

Subspace code constructions

Antonio Cossidente, Giuseppe Marino, Francesco Pavese

We improve on the lower bound of the maximum number of planes of $PG (8, q)$ mutually intersecting in at most one point leading to the following lower bound: ${\cal A}_q(9, 4;…

math.CO2019

On $q$ -covering designs

Francesco Pavese

A $q$ -covering design $C_{q} (n, k, r)$ , $k \geq r$ , is a collection $X$ of $(k - 1)$ -spaces of $PG (n - 1, q)$ such that every $(r - 1)$ -space of $\mathrm{PG}(n-1,…

math.CO2018

Cameron-Liebler line classes of $PG (3, q)$ admitting $PGL (2, q)$

Antonio Cossidente, Francesco Pavese

In this paper we describe an infinite family of Cameron-Liebler line classes of $PG (3, q)$ with parameter $(q^{2} + 1) /2$ , $q \equiv 1 (mod 4)$ . The example obtained admits ${\rm…

Zeros of special polynomials and their impact on a class of APN functions

On line-parallelisms of PG(3, q)

Strongly regular graphs from hyperbolic quadrics and their maximal cliques

Affine vector space partitions and spreads of quadrics

An infinite family of m-ovoids of the hyperbolic quadrics Q+(7,q)

On 4-general sets in finite projective spaces

On the geometry of the Hermitian Veronese curve and its quasi-Hermitian surfaces

The Geometry of (tmodq)-arcs

On the geometry of a (q+1)-arc of PG(3,q), q even

The m-ovoids of W(5,2)

On large partial ovoids of symplectic and Hermitian polar spaces

A modular equality for m-ovoids of elliptic quadrics

On near-MDS codes and caps

Small complete caps in PG(4n+1,q)

A clique-free pseudorandom subgraph of the pseudo polarity graph

On regular systems of finite classical polar spaces

Graphs cospectral with NU(n+1,q2), n=3

On cutting blocking sets and their codes

On symmetric and Hermitian rank distance codes

Combining subspace codes

On the PSU(4, 2)-invariant vertex-transitive strongly regular (216, 40, 4, 8) graph

Subspace code constructions

On q-covering designs

Cameron-Liebler line classes of PG(3,q) admitting PGL(2,q)

An infinite family of $m$ -ovoids of the hyperbolic quadrics $Q^{+} (7, q)$

The Geometry of $(t mod q)$ -arcs

On the geometry of a $(q + 1)$ -arc of $PG (3, q)$ , q even

The $m$ -ovoids of $W (5, 2)$

A modular equality for $m$ -ovoids of elliptic quadrics

Small complete caps in $PG (4 n + 1, q)$

Graphs cospectral with NU $(n + 1, q^{2})$ , $n \neq = 3$

On $q$ -covering designs

Cameron-Liebler line classes of $PG (3, q)$ admitting $PGL (2, q)$