M. Montanucci

activity

20152026

most citedA new family of maximal curves

28 citations · 86 across the 40 of their papers we have counts for

collaborators

56 papers

math.CO2026

Sunflowers of Reed--Solomon Codes

Roni Con, Anina Gruica, Maria Montanucci +1

We introduce and study Reed--Solomon sunflowers, namely families of Reed--Solomon codes whose pairwise intersections are all equal to the same fixed subspace. This notion lies at t…

math.AG2026

A maximal function field of genus $17$ over $F_{1 1^{2}}$

Peter Beelen, Maria Montanucci, Jonathan Niemann

In this article, we describe a new maximal function field $G$ over the finite field $F_{1 1^{2}}$ with $1 1^{2}$ elements and show that it cannot be obtained as a subfield of th…

cs.IT2026

Explicit and asymptotically good constructions of Algebraic Geometry codes in the sum-rank metric

Peter Beelen, Elena Berardini, Anina Gruica +1

Algebraic Geometry (AG) codes (i.e. linear codes from algebraic function fields) in the Hamming metric were proposed by Goppa in 1980 and have been intensively studied ever since.…

math.AG2026

On Weierstrass semigroups of maximal Fermat function fields

Peter Beelen, Maria Montanucci, Marie Frank vom Braucke

In this article we explicitly determine the Weierstrass semigroup at any place of some $F_{q^{2}}$ -maximal Fermat function fields $F_{m}$ , namely for $m = (q + 1) /2$ and…

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.AG2025

Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus, $q \equiv 0 (mod 3)$

Peter Beelen, Maria Montanucci, Lara Vicino

In this article we complete the work started in arXiv:2303.00376v1 [math.AG] and arXiv:2404.18808v1 [math.AG], explicitly determining the Weierstrass semigroup at any place and the…

cs.IT2025

Reed-Solomon Codes Against Insertions and Deletions: Full-Length and Rate- $1/2$ Codes

Peter Beelen, Roni Con, Anina Gruica +2

The performance of Reed--Solomon codes (RS codes, for short) in the presence of insertion and deletion errors has attracted growing attention in recent literature. In this work, we…

cs.IT2024

The Geometry of Codes for Random Access in DNA Storage

Anina Gruica, Maria Montanucci, Ferdinando Zullo

Effective and reliable data retrieval is critical for the feasibility of DNA storage, and the development of random access efficiency plays a key role in its practicality and relia…

math.AG2024

Intersection of irreducible curves and the Hermitian curve

Peter Beelen, Mrinmoy Datta, Maria Montanucci +1

Let $H_{q}$ denote the Hermitian curve in $P^{2}$ over $F_{q^{2}}$ and $C_{d}$ be an irreducible plane projective curve in $P^{2}$ also defined…

math.AG2024★ 1 cited

Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus, $q \equiv 1 (mod 3)$

Peter Beelen, Maria Montanucci, Lara Vicino

In this article we continue the work started in arXiv:2303.00376v1, explicitly determining the Weierstrass semigroup at any place and the full automorphism group of a known $\mathb…

math.NT2024

Some families of non-isomorphic maximal function fields

Peter Beelen, Maria Montanucci, Jonathan Tilling Niemann +1

The problem of understanding whether two given function fields are isomorphic is well-known to be difficult, particularly when the aim is to prove that an isomorphism does not exis…

math.AG2023

List-decoding of AG codes without genus penalty

Peter Beelen, Maria Montanucci

In this paper we consider algebraic geometry (AG) codes: a class of codes constructed from algebraic codes (equivalently, using function fields) by Goppa. These codes can be list-d…

math.AG2023★ 5 cited

Weierstrass semigroups and automorphism group of a maximal curve with the third largest genus

Peter Beelen, Maria Montanucci, Lara Vicino

In this article we explicitly determine the Weierstrass semigroup at any point and the full automorphism group of a known $F_{q^{2}}$ -maximal curve $X_{3}$ having th…

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

On the constant $D (q)$ defined by Homma

Peter Beelen, Maria Montanucci, Lara Vicino

Let $X$ be a projective, irreducible, nonsingular algebraic curve over the finite field $F_{q}$ with $q$ elements and let $∣ X (F_{q}) ∣$ and $g(\mat…

math.AG2021

Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve

M. Montanucci, G. Tizziotti

In this paper we determine the generalized Weierstrass semigroup $H (P_{\infty}, P_{1}, \dots, P_{m})$ , and consequently the Weierstrass semigroup $H(P_{\infty}, P_1, \ld…

math.NT2021

Classification of all Galois subcovers of the Skabelund maximal curves

Peter Beelen, Leonardo Landi, Maria Montanucci

In 2017 Skabelund constructed two new examples of maximal curves $S ~_{q}$ and $R ~_{q}$ as covers of the Suzuki and Ree curves, respectively. The resul…

math.AG2020★ 1 cited

A bound for the number of points of space curves over finite fields

Peter Beelen, Maria Montanucci

For a non-degenerate irreducible curve $C$ of degree $d$ in $P^{3}$ over $F_{q}$ , we prove that the number $N_{q} (C)$ of $F_{q}$ -rational points of $C$ satisfies…

math.AG2020

Weierstrass semigroups on the Skabelund maximal curve

Peter Beelen, Leonardo Landi, Maria Montanucci

In 2017, D. Skabelund constructed a maximal curve over $F_{q^{4}}$ as a cyclic cover of the Suzuki curve. In this paper we explicitly determine the structure of the Weierstr…

math.CO2020★ 5 cited

On a conjecture about maximum scattered subspaces of $F_{q^{6}} \times F_{q^{6}}$

Daniele Bartoli, Bence Csajbók, Maria Montanucci

Maximum scattered subspaces are not only objects of intrinsic interest in finite geometry but also powerful tools for the construction of MRD-codes, projective two-weight codes, an…

math.AG2020

Locally recoverable codes from automorphism groups of function fields of genus $g \geq 1$

Daniele Bartoli, Maria Montanucci, Luciane Quoos

A Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we hav…

math.AG2020

On algebraic curves with many automorphisms in characteristic p

Maria Montanucci

Let $X$ be an irreducible, non-singular, algebraic curve defined over a field of odd characteristic $p$ . Let $g$ and $γ$ be the genus and $p$ -rank of $X$ , respe…

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.AG2019

New examples of maximal curves with low genus

Daniele Bartoli, Massimo Giulietti, Mokoto Kawakita +1

We investigate the Jacobian decomposition of some algebraic curves over finite fields with genus $4$ , $5$ and $10$ . As a corollary, explicit equations for curves that are either ma…

Sunflowers of Reed--Solomon Codes

A maximal function field of genus 17 over F112​

Explicit and asymptotically good constructions of Algebraic Geometry codes in the sum-rank metric

On Weierstrass semigroups of maximal Fermat function fields

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

Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus, q≡0(mod3)

Reed-Solomon Codes Against Insertions and Deletions: Full-Length and Rate-1/2 Codes

The Geometry of Codes for Random Access in DNA Storage

Intersection of irreducible curves and the Hermitian curve

Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus, q≡1(mod3)

Some families of non-isomorphic maximal function fields

List-decoding of AG codes without genus penalty

Weierstrass semigroups and automorphism group of a maximal curve with the third largest genus

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

On the constant D(q) defined by Homma

Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve

Classification of all Galois subcovers of the Skabelund maximal curves

A bound for the number of points of space curves over finite fields

Weierstrass semigroups on the Skabelund maximal curve

On a conjecture about maximum scattered subspaces of Fq6​×Fq6​

Locally recoverable codes from automorphism groups of function fields of genus g≥1

On algebraic curves with many automorphisms in characteristic p

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

New examples of maximal curves with low genus

A maximal function field of genus $17$ over $F_{1 1^{2}}$

Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus, $q \equiv 0 (mod 3)$

Reed-Solomon Codes Against Insertions and Deletions: Full-Length and Rate- $1/2$ Codes

Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus, $q \equiv 1 (mod 3)$

On the constant $D (q)$ defined by Homma

On a conjecture about maximum scattered subspaces of $F_{q^{6}} \times F_{q^{6}}$

Locally recoverable codes from automorphism groups of function fields of genus $g \geq 1$