7 papers
Skew cyclic codes through Drinfeld modules
Giacomo Micheli, Mihran Papikian
We construct skew cyclic codes in the rank metric from the torsion of the supersingular Drinfeld module over , where is a root of a monic irreduci…
A General Construction of Codes from Drinfeld Modules
Alessandro Giannoni, Giacomo Micheli, Mihran Papikian
We construct additive rank-metric and sum-rank-metric codes from Drinfeld modules by restricting bounded-degree morphisms to prime-to-characteristic torsion. For supersingular Drin…
Rank metric codes from Drinfeld modules
Giacomo Micheli, Mihran Papikian
We establish a connection between Drinfeld modules and rank-metric codes, focusing on the case of semifield codes. Our method constructs rank-metric codes from linear subspaces of…
On the Riemann Hypothesis for Drinfeld Modules
Giacomo Micheli
In this paper we provide a short proof of the Riemann Hypothesis for Drinfeld modules which uses only basic notions from the theory of global function fields and of Drinfeld module…
Codes from -invariant polynomials
Giacomo Micheli, Vincenzo Pallozzi Lavorante, Phillip Waitkevich
Let be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on combined with the ide…
Optimal Rank-Metric Codes with Rank-Locality from Drinfeld Modules
Luca Bastioni, Mohamed O. Darwish, Giacomo Micheli
We introduce a new technique to construct rank-metric codes using the arithmetic theory of Drinfeld modules over global fields, and Dirichlet Theorem on polynomial arithmetic progr…
On rectangular unimodular matrices over the algebraic integers
Giacomo Micheli, Violetta Weger
Let and be positive integers such that . In this paper we compute the density of rectangular unimodular by matrices over the ring of algebraic integers of a nu…