L. Giuzzi

activity

20242026

collaborators

9 papers

math.CO2026

On minimal codes arising from projective embeddings of point-line geometries

Ilaria Cardinali, Luca Giuzzi

Let $C (I^c ◯)$ be the linear code arising from a projective system $I^c ◯$ of $PG (V) .$ Consider the point-line geometry $I^ = (P, L)$ and a project…

math.GR2025

On the $1$ -cohomology of $SL (n, K)$ on the dual of its adjoint module

Ilaria Cardinali, Luca Giuzzi, Antonio Pasini

Given a field $K$ , for any $n \geq 3$ the first cohomology group $H^{1} (G_{n}, A_{n}^{*})$ of the special linear group $G_{n} = SL (n, K)$ over the dual $A_{n}^{*}$ of its…

math.RT2025

The relatively universal cover of the natural embedding of the long root geometry for the group $SL (n + 1, K)$

I. Cardinali, L. Giuzzi, A. Pasini

The long root geometry $A_{n, {1, n}} (K)$ for the special linear group $SL (n + 1, K)$ admits an embedding in the (projective space of) the vector space of t…

math.CO2025

Linear codes arising from the point-hyperplane geometry-Part I: the Segre embedding

Ilaria Cardinali, Luca Giuzzi

Let $V$ be a vector space over the finite field $F_{q}$ with $q$ elements and $I^$ be the image of the Segre geometry $PG (V) \otimes PG (V^{*})$ in $\mathrm{PG}…

math.CO2025

Line Hermitian Grassmann Codes and their Parameters

Ilaria Cardinali, Luca Giuzzi

In this paper we introduce and study line Hermitian Grassmann codes as those subcodes of the Grassmann codes associated to the $2$ -Grassmannian of a Hermitian polar space defined o…

math.CO2025

Minimal codes from hypersurfaces in even characteristic

Angela Aguglia, Luca Giuzzi, Giovanni Longobardi +1

The setting of projective systems can be used to study the parameters of a projective linear code $C$ . This can be done by considering the intersections of the point set…

On minimal codes arising from projective embeddings of point-line geometries

On the 1-cohomology of SL(n,K) on the dual of its adjoint module

The relatively universal cover of the natural embedding of the long root geometry for the group SL(n+1,K)

Linear codes arising from the point-hyperplane geometry-Part I: the Segre embedding

Line Hermitian Grassmann Codes and their Parameters

Minimal codes from hypersurfaces in even characteristic

On the $1$ -cohomology of $SL (n, K)$ on the dual of its adjoint module

The relatively universal cover of the natural embedding of the long root geometry for the group $SL (n + 1, K)$