4 papers
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 . Two players alternately claim points, and the first player to occupy all points of…
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…
On the Characteristic Polynomial of Linearized Polynomials
Luca Bastioni, Giacomo Micheli, Shujun Zhao
Let be a finite field, and be a -linearized polynomial defined over of -degree (, with ). This paper provides an algorithm…
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…