Valentino Smaldore

activity

20202026

m

-ovoids in classical polar spaces

1 citations · 1 across the 17 of their papers we have counts for

collaborators

21 papers

math.CO2026

Construction of Regular Fat Linear Sets and Non-Representable q-Matroids

Yufei Qiu, Valentino Smaldore, Zhenpeng Wang +2

Let $q$ be a prime power. An $(r, i)$ -regular fat $F_{q}$ -linear set has exactly $r$ points of weight $i \geq 2$ , called fat points. All of its remaining points have weight one,…

math.CO2026

Vertex-transitive strongly regular graphs in the switching class of doubly transitive two-graphs

Robert F. Bailey, Gábor P. Nagy, Valentino Smaldore

Let $G$ be a permutation group that acts $2$ -transitively on the finite set $V$ and let $T = (V, T)$ be a two-graph whose automorphism group contains $G$ . In this paper, we…

math.CO2026

Classification of Deza graphs from anisotropic association schemes of quadrics

Valentino Smaldore

Let $Q^{ε} (3, q)$ , where $ε \in {+, -}$ and $q > 3$ is odd, be a non-degenerate hyperbolic or elliptic quadric of $P G (3, q)$ . Fix one of the two quadratic classes of a…

math.CO2026

Ramanujan polar graphs

Valentino Smaldore

Recently, a construction of minimal codes arising from a family of almost Ramanujan graphs was shown. Ramanujan graphs are examples of expander graphs that minimize the second-larg…

math.AG2026

Hermitian-Singer Functional and Differential Codes

Gábor Korchmáros, Federico Romaniello, Valentino Smaldore

Algebraic geometry codes on the Hermitian curve have been the subject of several papers, since they happen to have good performances and large automorphism groups. Here, those aris…

math.CO2025

Regular fat linear sets

Valentino Smaldore, Corrado Zanella, Ferdinando Zullo

In this work, we introduce $(r, i)$ -regular fat linear sets, which are defined as linear sets containing exactly $r$ points of weight $i$ and all other points of weight one. This no…

math.HO2025

List of constructions of $N O^{+} (6, 2)$

Valentino Smaldore

In this note, we list many equivalent constructions of the tangent polar graph $N O^{+} (6, 2)$ .

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

On Geometry and Combinatorics of Finite Classical Polar Spaces

Valentino Smaldore

Polar spaces over finite fields are fundamental in combinatorial geometry. The concept of polar space was firstly introduced by F. Veldkamp who gave a system of 10 axioms in the sp…

math.CO2024

New scattered linearized quadrinomials

Valentino Smaldore, Corrado Zanella, Ferdinando Zullo

Let $1 < t < n$ be integers, where $t$ is a divisor of $n$ . An R- $q^{t}$ -partially scattered polynomial is a $F_{q}$ -linearized polynomial $f$ in $F_{q^{n}} [X]$ that satisfie…

math.CO2024

Switching equivalence of strongly regular polar graphs

Gábor P. Nagy, Valentino Smaldore

We prove the switching equivalence of the strongly regular polar graphs $N O^{\pm} (4 m, 2)$ , $N O^{\mp} (2 m + 1, 4)$ , and $Γ (O^{\mp} (4 m, 2))$ plus an isolated vertex by giving an analytic descrip…

math.CO2024

On the stabilizer of the graph of linear functions over finite fields

Valentino Smaldore, Corrado Zanella, Ferdinando Zullo

In this paper we will study the action of $F_{q^{n}}^{2 \times 2}$ on the graph of an $F_{q}$ -linear function of $F_{q^{n}}$ into itself. In particular we will…

math.CO2023★ 1 cited

Some non-existence results on $m$ -ovoids in classical polar spaces

Jan De Beule, Jonathan Mannaert, Valentino Smaldore

In this paper we develop non-existence results for $m$ -ovoids in the classical polar spaces $Q^{-} (2 r + 1, q), W (2 r - 1, q)$ and $H (2 r, q^{2})$ for $r > 2$ . In [4] a lower bound on $m$ for the…

cs.IT2022

Bent functions and strongly regular graphs

Valentino Smaldore

The family of bent functions is a known class of Boolean functions, which have a great importance in cryptography. The Cayley graph defined on $Z_{2}^{n}$ by the support o…

math.CO2022

On a graph isomorphic to $N O^{+} (6, 2)$

Federico Romaniello, Valentino Smaldore

Let $Q^{+} (2 n - 1, 2)$ be a non-degenerate hyperbolic quadric of $P G (2 n - 1, 2)$ . Let $N O^{+} (2 n, 2)$ be the tangent graph, whose vertices are the points of $PG(2n-1,2) \setminus Q^{+}(2n…

math.CO2022

All minimal $[9, 4]_{2}$ -codes are hyperbolic quadrics

Valentino Smaldore

Minimal codes are being intensively studied in last years. $[n, k]_{q}$ -minimal linear codes are in bijection with strong blocking sets of size $n$ in $P G (k - 1, q)$ and a lower bound…

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

The Automorphism Group of $N U (3, q^{2})$

Federico Romaniello, Valentino Smaldore

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

math.CO2021

New hemisystems of the Hermitian surface

Vincenzo Pallozzi Lavorante, Valentino Smaldore

Finding Hemisystems is a challenging problem and just few examples arising from the Hermitian surface are known. A recent method to obtain Hemisystems is based on using maximal cur…

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 $P G (n, q^{2}) ∖ H (n, q^{2})$ …

Construction of Regular Fat Linear Sets and Non-Representable q-Matroids

Vertex-transitive strongly regular graphs in the switching class of doubly transitive two-graphs

Classification of Deza graphs from anisotropic association schemes of quadrics

Ramanujan polar graphs

Hermitian-Singer Functional and Differential Codes

Regular fat linear sets

List of constructions of NO+(6,2)

Strongly regular graphs from hyperbolic quadrics and their maximal cliques

On Geometry and Combinatorics of Finite Classical Polar Spaces

New scattered linearized quadrinomials

Switching equivalence of strongly regular polar graphs

On the stabilizer of the graph of linear functions over finite fields

Some non-existence results on m-ovoids in classical polar spaces

Bent functions and strongly regular graphs

On a graph isomorphic to NO+(6,2)

All minimal [9,4]2​-codes are hyperbolic quadrics

On large partial ovoids of symplectic and Hermitian polar spaces

The Automorphism Group of NU(3,q2)

New hemisystems of the Hermitian surface

On regular systems of finite classical polar spaces

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

List of constructions of $N O^{+} (6, 2)$

Some non-existence results on $m$ -ovoids in classical polar spaces

On a graph isomorphic to $N O^{+} (6, 2)$

All minimal $[9, 4]_{2}$ -codes are hyperbolic quadrics

The Automorphism Group of $N U (3, q^{2})$

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