106 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 , 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=
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
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
Unitals in with a large 2-point stabiliser
Let \cU be a unital embedded in the Desarguesian projective plane
\PG(2,q^2). Write for the subgroup of \PGL(3,q^2) which preserves
\cU. We show that \cU is classical if and only if \cU has two distinct
points for which the stabiliser has order .Comment: Revised version - clarified the case mu\neq\lambda^{q+1} - 7 page
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
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