A. Giannoni

activity

20232026

collaborators

Showing 2026Show all

8 papers · 1 filter

math.CO2026

The weak cylinder conjecture for polynomial graphs of bounded degree

Daniele Bartoli, Alessandro Giannoni

Ball's weak cylinder conjecture asserts that a set of $p^{2}$ points in $AG (3, p)$ with at least $p$ non-determined directions is a union of $p$ parallel lines. We prove the…

math.CO2026

Maximum 2-scattered subspaces of $V (r, q^{6})$ for every $r \geq 3$

Daniele Bartoli, Francesco Ghiandoni, Alessandro Giannoni +2

We prove that for every prime power $q$ and every integer $r \geq 3$ there exists a maximum $2$ -scattered $F_{q}$ -subspace of $V (r, q^{6})$ , that is, a $2 r$ -dimensional $\mathbb…

math.NT2026

F-sets of arbitrary finite width

Alessandro Giannoni

Ferraguti and Micheli conjectured that non-trivial $F$ -sets of every prescribed width exist over each finite field. We prove the finite-width part of their conjecture over $\mathbb…

math.NT2026

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…

math.CO2026

The extremal gap for scattered $q$ -systems

Alessandro Giannoni

Two general estimates govern the rank of an $h$ -scattered $q$ -system: the scattered upper bound and the lower bound for systems maximal under inclusion. We determine exactly when t…

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…

cs.IT2026

An infinite family of non-extendable MRD codes

Daniele Bartoli, Alessandro Giannoni, Giuseppe Marino +1

In the realm of rank-metric codes, Maximum Rank Distance (MRD) codes are optimal algebraic structures attaining the Singleton-like bound. A major open problem in this field is dete…

math.CO2026

Generalizing a family of scattered quadrinomials in $F_{q^{2 t}} [X]$

Alessandro Giannoni, Giovanni Giuseppe Grimaldi, Giovanni Longobardi +1

In recent years, several efforts have focused on identifying new families of scattered polynomials. Currently, only three families in $F_{q^{n}} [X]$ are known to exist for i…

The weak cylinder conjecture for polynomial graphs of bounded degree

Maximum 2-scattered subspaces of V(r,q6) for every r≥3

F-sets of arbitrary finite width

A General Construction of Codes from Drinfeld Modules

The extremal gap for scattered q-systems

Thresholds for Tic-Tac-Toe on Finite Affine Spaces

An infinite family of non-extendable MRD codes

Generalizing a family of scattered quadrinomials in Fq2t​[X]

Maximum 2-scattered subspaces of $V (r, q^{6})$ for every $r \geq 3$

The extremal gap for scattered $q$ -systems

Generalizing a family of scattered quadrinomials in $F_{q^{2 t}} [X]$