From the 1 of 6 linked papers with an AI index.
6 papers
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…
Homomorphic encryption schemes based on coding theory and polynomials
Giovanni Giuseppe Grimaldi
Homomorphic encryption is a powerful cryptographic tool that enables secure computations on the private data. It evaluates any function for any operation securely on the encrypted…
On the hull of linearized polynomial codes
Daniele Bartoli, Giovanni Giuseppe Grimaldi, Pantelimon StÄnicÄ
Motivated by entanglement-assisted quantum error-correcting codes, where the hull dimension determines the number of required pre-shared entangled pairs, we study hulls of two fami…
On the Classification of Dillon's APN Hexanomials
Daniele Bartoli, Giovanni Giuseppe Grimaldi, Pantelimon Stanica
We systematically analyze a class of hexanomial functions over finite fields of characteristic proposed by Dillon (2006) as candidates for almost perfect nonlinear (APN) functi…
A geometric characterization of known maximum scattered linear sets of
Giovanni Giuseppe Grimaldi, Somi Gupta, Giovanni Longobardi +1
An - linear set of is a set of points defined by non-zero vectors of an -subspa…
Non-linear MRD codes from cones over exterior sets
Nicola Durante, Giovanni Giuseppe Grimaldi, Giovanni Longobardi
By using the notion of -embedding of a (canonical) subgeometry and of exterior set with respect to the -secant variety of a subset $\mathcal{A…