Jonathan Niemann

collaborators

6 papers

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…

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…

cs.IT2026

Serving Every Symbol: All-Symbol PIR and Batch Codes

Avital Boruchovsky, Anina Gruica, Jonathan Niemann +1

A $t$ -all-symbol PIR code and a $t$ -all-symbol batch code of dimension $k$ consist of $n$ servers storing linear combinations of $k$ information symbols with the following recovery…

math.NT2024

Non-isomorphic maximal function fields of genus $q - 1$

Jonathan Niemann

The classification of maximal function fields over a finite field is a difficult open problem, and even determining isomorphism classes among known function fields is challenging i…

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.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…