10 papers
The weak cylinder conjecture for polynomial graphs of bounded degree
Daniele Bartoli, Alessandro Giannoni
Ball's weak cylinder conjecture asserts that a set of points in with at least non-determined directions is a union of parallel lines. We prove the…
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…
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…
On -dimensional MRD codes of type
Daniele Bartoli, Francesco Ghiandoni
In this work we present results on the classification of -linear MRD codes of dimension three. In particular, using connections with certain algebraic varieties o…
A new family of -scattered subspaces and related MRD codes
Daniele Bartoli, Francesco Ghiandoni, Alessandro Giannoni +1
Scattered subspaces and -scattered subspaces have been extensively studied in recent decades for both theoretical purposes and their connections to various applications. While n…
New scattered subspaces in higher dimensions
D. Bartoli, A. Giannoni, G. Marino
Over the past few decades, there has been extensive research on scattered subspaces, partly because of their link to MRD codes. These subspaces can be characterized using linearize…