6 papers · 1 filter
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…
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…