Luca Bastioni

activity

20232026

collaborators

5 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…

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…

cs.IT2024

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.CO2023

On complete $m$ -arcs

Luca Bastioni, Giacomo Micheli

Let $m$ be a positive integer and $q$ be a prime power. For large finite base fields $F_{q}$ , we show that any curve can be used to produce a complete $m$ -arc as long as some…