67 research outputs found
On some subvarieties of the Grassmann variety
Let be a Desarguesian --spread of , a
-dimensional subspace of and the linear set
consisting of the elements of with non-empty intersection with
. It is known that the Pl\"{u}cker embedding of the elements of is a variety of , say . In this paper, we
describe the image under the Pl\"{u}cker embedding of the elements of
and we show that it is an -dimensional algebraic variety, projection of a
Veronese variety of dimension and degree , and it is a suitable linear
section of .Comment: Keywords: Grassmannian, linear set, Desarguesian spread, Schubert
variet
Intersections of the Hermitian Surface with irreducible Quadrics in even Characteristic
We determine the possible intersection sizes of a Hermitian surface with an irreducible quadric of sharing at least a
tangent plane at a common non-singular point when is even.Comment: 20 pages; extensively revised and corrected version. This paper
extends the results of arXiv:1307.8386 to the case q eve
Intersections of the Hermitian surface with irreducible quadrics in , odd
In , with odd, we determine the possible intersection sizes of
a Hermitian surface and an irreducible quadric
having the same tangent plane at a common point .Comment: 14 pages; clarified the case q=
Intersection sets, three-character multisets and associated codes
In this article we construct new minimal intersection sets in
sporting three intersection numbers with hyperplanes; we
then use these sets to obtain linear error correcting codes with few weights,
whose weight enumerator we also determine. Furthermore, we provide a new family
of three-character multisets in with even and we
also compute their weight distribution.Comment: 17 Pages; revised and corrected result
Minimum distance of Symplectic Grassmann codes
We introduce the Symplectic Grassmann codes as projective codes defined by
symplectic Grassmannians, in analogy with the orthogonal Grassmann codes
introduced in [4]. Note that the Lagrangian-Grassmannian codes are a special
class of Symplectic Grassmann codes. We describe the weight enumerator of the
Lagrangian--Grassmannian codes of rank and and we determine the minimum
distance of the line Symplectic Grassmann codes.Comment: Revised contents and biblograph
Implementing Line-Hermitian Grassmann codes
In [I. Cardinali and L. Giuzzi. Line Hermitian Grassmann codes and their
parameters. Finite Fields Appl., 51: 407-432, 2018] we introduced line
Hermitian Grassmann codes and determined their parameters. The aim of this
paper is to present (in the spirit of [I. Cardinali and L. Giuzzi. Enumerative
coding for line polar Grassmannians with applications to codes. Finite Fields
Appl., 46:107-138, 2017]) an algorithm for the point enumerator of a line
Hermitian Grassmannian which can be usefully applied to get efficient encoders,
decoders and error correction algorithms for the aforementioned codes.Comment: 26 page
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