Barbara Gatti

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20242026

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math.AG2026

Evaluation codes from linear systems of conics

Barbara Gatti, Gábor Korchmáros, Gioia Schulte

The Datta-Johnsen code is an evaluation code where the linear combinations of elementary symmetric polynomials are evaluated on the set of all points with pairwise distinct coordin…

math.AG2025

Evaluation codes arising from symmetric polynomials

Barbara Gatti, Gábor Korchmáros, Gábor P. Nagy +2

Datta and Johnsen (Des. Codes and Cryptogr., {\bf{91}} (2023), 747-761) introduced a new family of evalutation codes in an affine space of dimension $\geq 2$ over a finite field $\m…

math.AG2024

On a Galois cover of the Hermitian curve of genus $g = \frac{1}{8} (q - 1)^{2}$

Barbara Gatti, Gioia Schulte

In the study of algebraic curves with many points over a finite field, a well known general problem is to understanding better the properties of $F_{q^{2}}$ -maximal curves w…

math.AG2024

Galois subcovers of the Hermitian curve in characteristic $p$ with respect to subgroups of order $d p$ with $d \neq = p$ prime

Arianna Dionigi, Barbara Gatti

A problem of current interest, also motivated by applications to Coding theory, is to find explicit equations for \textit{maximal} curves, that are projective, geometrically irredu…

math.AG2023

Galois subcovers of the Hermitian curve in characteristic $p$ with respect to subgroups of order $p^{2}$

Barbara Gatti, Gábor Korchmáros

A (projective, geometrically irreducible, non-singular) curve $X$ defined over a finite field $F_{q^{2}}$ is maximal if the number $N_{q^{2}}$ of its $\mathbb{F}_{q^…

Evaluation codes from linear systems of conics

Evaluation codes arising from symmetric polynomials

On a Galois cover of the Hermitian curve of genus g=81​(q−1)2

Galois subcovers of the Hermitian curve in characteristic p with respect to subgroups of order dp with d=p prime

Galois subcovers of the Hermitian curve in characteristic p with respect to subgroups of order p2

On a Galois cover of the Hermitian curve of genus $g = \frac{1}{8} (q - 1)^{2}$

Galois subcovers of the Hermitian curve in characteristic $p$ with respect to subgroups of order $d p$ with $d \neq = p$ prime

Galois subcovers of the Hermitian curve in characteristic $p$ with respect to subgroups of order $p^{2}$