5 papers
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…
Zeros of special polynomials and their impact on a class of APN functions
Daniele Bartoli, Marco Calderini, Giuseppe Marino +1
In 2021, Calderini et al. introduced a construction for APN functions on in bivariate form $$ f(x,y)=\big(xy,\, x^{2^r+1} + x^{2^{r+m/2}} y^{2^{m/2}} + bxy^{2…
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…
Linear rank-metric intersecting codes
Daniele Bartoli, Martino Borello, Giuseppe Marino +1
In this paper we introduce and investigate rank-metric intersecting codes, a new class of linear codes in the rank-metric context, inspired by the well-studied notion of intersecti…
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…