G. Zini

activity

20152026

most citedAlgebraic Geometric codes from Kummer Extensions

3 citations · 18 across the 26 of their papers we have counts for

collaborators

36 papers

math.AG2026

Double Artin-Schreier extensions of rational function fields with many lifted automorphisms

Herivelto Borges, Jonathan Niemann, Giovanni Zini

In this paper we investigate algebraic function fields in positive characteristic mainly obtained as double Artin-Schreier extensions of rational function fields with a plane model…

math.AG2025

Non-isomorphic subfields of the BM and GGS maximal function fields

Peter Beelen, Tobias Drue, Maria Montanucci +1

In 2016 Tafazolian et al. introduced new families of $F_{q^{2 n}}$ -maximal function fields $Y_{n, s}$ and $X_{n, s, a, b}$ arising as subfields of the first…

math.AG2023

On the automorphism group of a family of maximal curves not covered by the Hermitian curve

Maria Montanucci, Guilherme Tizziotti, Giovanni Zini

In this paper we compute the automorphism group of the curves $X_{a, b, n, s}$ and $Y_{n, s}$ introduced in Tafazolian et al. in 2016 as new examples of maximal cur…

math.NT2022★ 2 cited

Towards the classification of exceptional scattered polynomials

Daniele Bartoli, Massimo Giulietti, Giovanni Zini

Scattered polynomials over finite fields attracted an increasing attention in the last years. One of the reasons is their deep connection with Maximum Rank Distance (MRD) codes. Kn…

math.GR2022★ 1 cited

On ideals in group algebras: an uncertainty principle and the Schur product

Martino Borello, Wolfgang Willems, Giovanni Zini

In this paper we investigate some properties of ideals in group algebras of finite groups over fields. First, we highlight an important link between their dimension, their minimal…

cs.IT2022

Non-minimum tensor rank Gabidulin codes

Daniele Bartoli, Giovanni Zini, Ferdinando Zullo

The tensor rank of some Gabidulin codes of small dimension is investigated. In particular, we determine the tensor rank of any rank metric code equivalent to an $8$ -dimensional $\m…

cs.IT2021

Linear maximum rank distance codes of exceptional type

Daniele Bartoli, Giovanni Zini, Ferdinando Zullo

Scattered polynomials of a given index over finite fields are intriguing rare objects with many connections within mathematics. Of particular interest are the exceptional ones, as…

math.CO2021★ 1 cited

On a family of linear MRD codes with parameters $[8 \times 8, 16, 7]_{q}$

Marco Timpanella, Giovanni Zini

In this paper we consider a family $F$ of $16$ -dimensional $F_{q}$ -linear rank metric codes in $F_{q}^{8 \times 8}$ , arising from the polynomial $x^{q^s}+δx^{…

math.CO2021

Investigating the exceptionality of scattered polynomials

Daniele Bartoli, Giovanni Zini, Ferdinando Zullo

Scattered polynomials over a finite field $F_{q^{n}}$ have been introduced by Sheekey in 2016, and a central open problem regards the classification of those that are except…

math.CO2020

$r$ -fat linearized polynomials over finite fields

Daniele Bartoli, Giacomo Micheli, Giovanni Zini +1

In this paper we prove that the property of being scattered for a $F_{q}$ -linearized polynomial of small $q$ -degree over a finite field $F_{q^{n}}$ is unstable, in th…

math.CO2020

Scattered subspaces and related codes

Giovanni Zini, Ferdinando Zullo

After a seminal paper by Shekeey (2016), a connection between maximum $h$ -scattered $F_{q}$ -subspaces of $V (r, q^{n})$ and maximum rank distance (MRD) codes has been establishe…

math.CO2020★ 1 cited

On certain linearized polynomials with high degree and kernel of small dimension

Olga Polverino, Giovanni Zini, Ferdinando Zullo

Let $f$ be the $F_{q}$ -linear map over $F_{q^{2 n}}$ defined by $x \mapsto x + a x^{q^{s}} + b x^{q^{n + s}}$ with $g cd (n, s) = 1$ . It is known that the kernel of $f$ has dimensi…

math.CO2020

On the intersection problem for linear sets in the projective line

Giovanni Zini, Ferdinando Zullo

The aim of this paper is to investigate the intersection problem between two linear sets in the projective line over a finite field. In particular, we analyze the intersection betw…

math.GR2020★ 1 cited

On two Möbius function for a finite non-solvable group

Francesca Dalla Volta, Giovanni Zini

Let $G$ be a finite group, $μ$ be the Möbius function on the subgroup lattice of $G$ , and $λ$ be the Möbius function on the poset of conjugacy classes of subgroups of $G$ . It was p…

math.CO2020

Linear sets from projection of Desarguesian spreads

Vito Napolitano, Olga Polverino, Giovanni Zini +1

Every linear set in a Galois space is the projection of a subgeometry, and most known characterizations of linear sets are given under this point of view. For instance, scattered l…

math.AG2019

On certain self-orthogonal AG codes with applications to Quantum error-correcting codes

Daniele Bartoli, Maria Montanucci, Giovanni Zini

In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar pro…

math.GR2019

The Möbius function of $PSL (3, 2^{p})$ for any prime $p$

Martino Borello, Francesca Dalla Volta, Giovanni Zini

Let $G$ be the simple group $PSL (3, 2^{p})$ , where $p$ is a prime number. For any subgroup $H$ of $G$ , we compute the Möbius function of $H$ in the subgroup lattice of $G$ . To t…

math.CO2019★ 1 cited

Bent functions from triples of permutation polynomials

Daniele Bartoli, Maria Montanucci, Giovanni Zini

We provide constructions of bent functions using triples of permutations. This approach is due to Mesnager. In general, involutions have been mostly considered in such a machinery;…

math.CO2018

Weierstrass semigroups at every point of the Suzuki curve

Daniele Bartoli, Maria Montanucci, Giovanni Zini

In this article we explicitly determine the structure of the Weierstrass semigroups $H (P)$ for any point $P$ of the Suzuki curve $S_{q}$ . As the point $P$ varies, exactly t…

math.CO2018

The Möbius function of $PSU (3, 2^{2^{n}})$

Giovanni Zini

Let $G$ be the simple group $PSU (2, 2^{2^{n}})$ , $n > 0$ . For any subgroup $H$ of $G$ , we compute the Möbius function $μ_{L} (H, G)$ of $H$ in the subgroup lattice $L$ of $G$ , and the…

math.AG2018★ 2 cited

The complete list of genera of quotients of the $F_{q^{2}}$ -maximal Hermitian curve for $q \equiv 1 (mod 4)$

Maria Montanucci, Giovanni Zini

Let $F_{q^{2}}$ be the finite field with $q^{2}$ elements. Most of the known $F_{q^{2}}$ -maximal curves arise as quotient curves of the $F_{q^{2}}$ -maximal Hermi…

math.AG2018

On the classification problem for the genera of quotients of the Hermitian curve

Francesca Dalla Volta, Maria Montanucci, Giovanni Zini

In this paper we characterize the genera of those quotient curves $H_{q} / G$ of the $F_{q^{2}}$ -maximal Hermitian curve $H_{q}$ for which $G$ is contained in…

math.AG2018★ 1 cited

Quotients of the Hermitian curve from subgroups of $PGU (3, q)$ without fixed points or triangles

Maria Montanucci, Giovanni Zini

In this paper we deal with the problem of classifying the genera of quotient curves $H_{q} / G$ , where $H_{q}$ is the $F_{q^{2}}$ -maximal Hermitian curve and $…

cs.IT2017

AG codes and AG quantum codes from cyclic extensions of the Suzuki and Ree curves

Maria Montanucci, Marco Timpanella, Giovanni Zini

We investigate several types of linear codes constructed from two families $S ~_{q}$ and $R ~_{q}$ of maximal curves over finite fields recently construct…

Double Artin-Schreier extensions of rational function fields with many lifted automorphisms

Non-isomorphic subfields of the BM and GGS maximal function fields

On the automorphism group of a family of maximal curves not covered by the Hermitian curve

Towards the classification of exceptional scattered polynomials

On ideals in group algebras: an uncertainty principle and the Schur product

Non-minimum tensor rank Gabidulin codes

Linear maximum rank distance codes of exceptional type

On a family of linear MRD codes with parameters [8×8,16,7]q​

Investigating the exceptionality of scattered polynomials

r-fat linearized polynomials over finite fields

Scattered subspaces and related codes

On certain linearized polynomials with high degree and kernel of small dimension

On the intersection problem for linear sets in the projective line

On two Möbius function for a finite non-solvable group

Linear sets from projection of Desarguesian spreads

On certain self-orthogonal AG codes with applications to Quantum error-correcting codes

The Möbius function of PSL(3,2p) for any prime p

Bent functions from triples of permutation polynomials

Weierstrass semigroups at every point of the Suzuki curve

The Möbius function of PSU(3,22n)

The complete list of genera of quotients of the Fq2​-maximal Hermitian curve for q≡1(mod4)

On the classification problem for the genera of quotients of the Hermitian curve

Quotients of the Hermitian curve from subgroups of PGU(3,q) without fixed points or triangles

AG codes and AG quantum codes from cyclic extensions of the Suzuki and Ree curves

On a family of linear MRD codes with parameters $[8 \times 8, 16, 7]_{q}$

$r$ -fat linearized polynomials over finite fields

The Möbius function of $PSL (3, 2^{p})$ for any prime $p$

The Möbius function of $PSU (3, 2^{2^{n}})$

The complete list of genera of quotients of the $F_{q^{2}}$ -maximal Hermitian curve for $q \equiv 1 (mod 4)$

Quotients of the Hermitian curve from subgroups of $PGU (3, q)$ without fixed points or triangles