Luca Giuzzi

Codes and caps from orthogonal Grassmannians

In this paper we investigate linear error correcting codes and projective caps related to the Grassmann embedding e 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 e 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 e k gr is a projective cap.

Algebraic curves and maximal arcs

AbstractA lower bound on the minimum degree of the plane algebraic curves containing every point in a large point-set

Enumerative coding for line polar Grassmannians with applications to codes

\mathcal{K}

Minimum distance of Orthogonal Line-Grassmann Codes in even characteristic

of the Desarguesian plane PG(2,q) is obtained. The case where

Families of twisted tensor product codes

\mathcal{K}

Constructions of unitals in Desarguesian planes

is a maximal (k,n)-arc is considered in greater depth.

LDPC codes from Singer cycles

A

On transparent embeddings of point-line geometries

k

Line Hermitian Grassmann codes and their parameters

-polar Grassmannian is the geometry having as pointset the set of all

Intersections of the Hermitian surface with irreducible quadrics in PG(3 ,q2), q odd

k