From the 1 of 7 linked papers with an AI index.
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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…
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…
A new infinite family of maximum -scattered -subspaces of and associated MRD codes
Daniele Bartoli, Alessandro Giannoni, Giuseppe Marino
The exploration of linear subspaces, particularly scattered subspaces, has garnered considerable attention across diverse mathematical disciplines in recent years, notably within f…