From the 1 of 6 linked papers with an AI index.
6 papers
The extremal gap for scattered -systems
Alessandro Giannoni
Two general estimates govern the rank of an -scattered -system: the scattered upper bound and the lower bound for systems maximal under inclusion. We determine exactly when t…
Generalizing a family of scattered quadrinomials in
Alessandro Giannoni, Giovanni Giuseppe Grimaldi, Giovanni Longobardi +1
The paper establishes sufficient conditions under which a family of quadrinomials over finite fields are scattered, extending previously known families and analyzing their equivale…
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…
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…
Long QMDS additive code
Daniele Bartoli, Alessandro Giannoni, Giuseppe Marino +1
We investigate additive codes, defined as -linear subspaces of length and dimension over . An additive code is…
Towards the classification of scattered binomials
Daniele Bartoli, Francesco Ghiandoni, Alessandro Giannoni +1
Let \( q \) be a prime power and \( n \) an integer. An \( \mathbb{F}_q \)-linearized polynomial \( f \) is said to be scattered if it satisfies the condition that for all \( x, y…