G. Micheli

activity

20172021

most citedIrreducible polynomials over finite fields produced by composition of quadratics

6 citations · 6 across the 3 of their papers we have counts for

collaborators

13 papers

cs.IT2021

Optimal Selection for Good Polynomials of Degree up to Five

Austin Dukes, Andrea Ferraguti, Giacomo Micheli

Good polynomials are the fundamental objects in the Tamo-Barg constructions of Locally Recoverable Codes (LRC). In this paper we classify all good polynomials up to degree $5$ , pro…

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.NT2020

Local to global principle for expected values

Giacomo Micheli, Severin Schraven, Violetta Weger

This paper constructs a new local to global principle for expected values over free $Z$ -modules of finite rank. In our strategy we use the same philosophy as Ekedhal's Sie…

math.CO2020

Algebraic constructions of complete $m$ -arcs

Daniele Bartoli, Giacomo Micheli

Let $m$ be a positive integer, $q$ be a prime power, and $PG (2, q)$ be the projective plane over the finite field $F_{q}$ . Finding complete $m$ -arcs in $\mathrm{PG}(2…

math.NT2020

Exceptional scatteredness in prime degree

Andrea Ferraguti, Giacomo Micheli

Let $q$ be an odd prime power and $n$ be a positive integer. Let $ℓ \in F_{q^{n}} [x]$ be a $q$ -linearised $t$ -scattered polynomial of linearized degree $r$ . Let $d=\max\{t,…

math.NT2019

The Algebraic Theory of Fractional Jumps

Dorian Goldfeld, Giacomo Micheli

In this paper we start by briefly surveying the theory of Fractional Jumps and transitive projective maps. Then, we give an efficient construction of a fractional jump of a project…