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Luca Giuzzi

Publications and source records attributed to Luca Giuzzi.

42 records · Page 3Linked to original sources
arXiv2014

On some subvarieties of the Grassmann variety

Let $\mathcal S$ be a Desarguesian $(t-1)$--spread of $PG(rt-1,q)$, $Π$ a $m$-dimensional subspace of $PG(rt-1,q)$ and $Λ$ the linear set consisting of the elements of $\mathcal S$ with non-empty intersection with $Π$. It is known that the Plücker embedding of the elements of $\mathcal S$ is a variety of $PG(r^t-1,q)$, say ${\mathcal V}_{rt}$. In this paper, we describe the image under the Plücker embedding of the elements of $Λ$ and we show that it is an $m$-dimensional algebraic variety, projection of a Veronese variety of dimension $m$ and degree $t$, and it is a suitable linear section of ${\mathcal V}_{rt}$.

math.CO↗
arXiv2013

Codes and caps from orthogonal Grassmannians

In this paper we investigate linear error correcting codes and projective caps related to the Grassmann embedding $\varepsilon_k^{gr}$ of an orthogonal Grassmannian $Δ_k$. In particular, we determine some of the parameters of the codes arising from the projective system determined by $\varepsilon_k^{gr}(Δ_k)$. We also study special sets of points of $Δ_k$ which are met by any line of $Δ_k$ in at most 2 points and we show that their image under the Grassmann embedding $\varepsilon_k^{gr}$ is a projective cap.

math.AG↗
arXiv2011

Families of twisted tensor product codes

Using geometric properties of the variety $\cV_{r,t}$, the image under the Grassmannian map of a Desarguesian $(t-1)$-spread of $\PG(rt-1,q)$, we introduce error correcting codes related to the twisted tensor product construction, producing several families of constacyclic codes. We exactly determine the parameters of these codes and characterise the words of minimum weight.

math.CO↗
arXiv2011

New results on path-decompositions and their down-links

In (arXiv:1004.4127) the concept of down-link from a (K_v, G)-design B to a (K_n, G')-design B' has been introduced. In the present paper the spectrum problems for G'= P4 are studied. General results on the existence of path-decompositions and embeddings between path- decompositions playing a fundamental role for the construction of down-links are also presented

math.CO↗
arXiv2011

Down-linking $(K_v,Γ)$-designs to $P_3$-designs

Let G' be a subgraph of a graph G. We define a down-link from a (K_v,G)-design B to a (K_n,G')-design B' as a map f:B->B' mapping any block of B into one of its subgraphs. This is a new concept, closely related with both the notion of metamorphosis and that of embedding. In the present paper we study down-links in general and prove that any (K_v,G)-design might be down-linked to a (K_n,G')-design, provided that n is admissible and large enough. We also show that if G'=P_3, it is always possible to find a down-link to a design of order at most v+3. This bound is then improved for several classes of graphs Gamma, by providing explicit constructions.

math.CO↗