54 research outputs found
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
-Intersection sets in and two-character multisets in
In this article we construct new minimal intersection sets in
with respect to hyperplanes, of size and multiplicity , where
rt \in \ q^2r-3-q^(3r-4)/2, q^2r-3-q^r-2\rqPG(3,q^2)AG(r,q^2)$ satisfying the opposite of the algebraic conditions required in [1]
for quasi--Hermitian varieties
Maximum number of points on intersection of a cubic surface and a non-degenerate Hermitian surface
In 1991 S{\o}rensen proposed a conjecture for the maximum number of points on
the intersection of a surface of degree and a non-degenerate Hermitian
surface in \PP^3(\Fqt). The conjecture was proven to be true by Edoukou in
the case when . In this paper, we prove that the conjecture is true for
and . We further determine the second highest number of rational
points on the intersection of a cubic surface and a non-degenerate Hermitian
surface. Finally, we classify all the cubic surfaces that admit the highest and
second highest number of points in common with a non-degenerate Hermitian
surface. This classifications disproves one of the conjectures proposed by
Edoukou, Ling and Xing
Partial ovoids and partial spreads in finite classical polar spaces
We survey the main results on ovoids and spreads, large maximal partial ovoids and large maximal partial spreads, and on small maximal partial ovoids and small maximal partial spreads in classical finite polar spaces. We also discuss the main results on the spectrum problem on maximal partial ovoids and maximal partial spreads in classical finite polar spaces
On regular sets of affine type in finite Desarguesian planes and related codes
In this paper, we consider point sets of finite Desarguesian planes whose
multisets of intersection numbers with lines is the same for all but one
exceptional parallel class of lines. We call such sets regular of affine type.
When the lines of the exceptional parallel class have the same intersection
numbers, then we call these sets regular of pointed type. Classical examples
are e.g. unitals; a detailed study and constructions of such sets with few
intersection numbers is due to Hirschfeld and Sz\H{o}nyi from 1991. We here
provide some general construction methods for regular sets and describe a few
infinite families. The members of one of these families have the size of a
unital and meet affine lines of in one of possible
intersection numbers, each of them congruent to modulo . As a
byproduct, we determine the intersection sizes of the Hermitian curve defined
over with suitable rational curves of degree and
we obtain -divisible codes with non-zero weights. We also
determine the weight enumerator of the codes arising from the general
constructions modulus some -powers.Comment: 16 pages/revised and improved versio
On -ovoids of with odd
In this paper, we provide a construction of -ovoids of the hyperbolic
quadric , an odd prime power, by glueing -ovoids of the
elliptic quadric . This is possible by controlling some intersection
properties of (putative) -ovoids of elliptic quadrics. It yields eventually
-ovoids of not coming from a -system. Secondly, we also
construct -ovoids for in . Therefore we
first investigate how to construct spreads of \pg(3,q) that have as many
secants to an elliptic quadric as possible
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