Daniele Bartoli

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20242026

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math.CO2024

A new infinite family of maximum $h$ -scattered $F_{q}$ -subspaces of $V (m (h + 1), q^{n})$ 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…

cs.IT2024

On $3$ -dimensional MRD codes of type $⟨ x^{q^{t}}, x + δ x^{q^{2 t}}, G (x)⟩$

Daniele Bartoli, Francesco Ghiandoni

In this work we present results on the classification of $F_{q^{n}}$ -linear MRD codes of dimension three. In particular, using connections with certain algebraic varieties o…

math.CO2024

A new family of $2$ -scattered subspaces and related MRD codes

Daniele Bartoli, Francesco Ghiandoni, Alessandro Giannoni +1

Scattered subspaces and $h$ -scattered subspaces have been extensively studied in recent decades for both theoretical purposes and their connections to various applications. While n…

math.CO2024

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…

A new infinite family of maximum h-scattered Fq​-subspaces of V(m(h+1),qn) and associated MRD codes

On 3-dimensional MRD codes of type ⟨xqt,x+δxq2t,G(x)⟩

A new family of 2-scattered subspaces and related MRD codes

New scattered subspaces in higher dimensions

A new infinite family of maximum $h$ -scattered $F_{q}$ -subspaces of $V (m (h + 1), q^{n})$ and associated MRD codes

On $3$ -dimensional MRD codes of type $⟨ x^{q^{t}}, x + δ x^{q^{2 t}}, G (x)⟩$

A new family of $2$ -scattered subspaces and related MRD codes