Luca Bastioni

collaborators

4 papers

math.CO2026

Thresholds for Tic-Tac-Toe on Finite Affine Spaces

Luca Bastioni, Alessandro Giannoni, Javier Lobillo-Olmedo

We introduce an affine version of Tic-Tac-Toe played on the finite affine space $F_{q}^{m}$ . Two players alternately claim points, and the first player to occupy all points of…

quant-ph2026

Climbing the Clifford Hierarchy

Luca Bastioni, Samuel Glandon, Tefjol Pllaha +2

The Clifford Hierarchy has been a central topic in quantum computation due to its strong connections with fault-tolerant quantum computation, magic state distillation, and more. Ne…

cs.IT2026

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…

math.NT2025

On the Characteristic Polynomial of Linearized Polynomials

Luca Bastioni, Giacomo Micheli, Shujun Zhao

Let $k$ be a finite field, and $L$ be a $q$ -linearized polynomial defined over $k$ of $q$ -degree $r$ ( $L = \sum_{i = 0}^{r} a_{i} Z^{q^{i}}$ , with $a_{i} \in k$ ). This paper provides an algorithm…