210 research outputs found
On -covering designs
A -covering design , , is a collection
of -spaces of such that every
-space of is contained in at least one element of
. Let denote the minimum number of
-spaces in a -covering design . In this paper
improved upper bounds on , ,
, , and , , are presented. The results are achieved by constructing the related
-covering designs
Subspace code constructions
We improve on the lower bound of the maximum number of planes of mutually intersecting in at most one point leading to the following
lower bound: for
constant dimension subspace codes. We also construct two new non-equivalent
constant dimension subspace orbit-codes
On 4-general sets in finite projective spaces
A -general set in is a set of points of
spanning the whole and such that no four of them are on a
plane. Such a pointset is said to be complete if it is not contained in a
larger -general set of . In this paper upper and lower
bounds for the size of the largest and the smallest complete -general set in
, respectively, are investigated. Complete -general sets in
, , whose size is close to the theoretical upper
bound are provided. Further results are also presented, including a description
of the complete -general sets in projective spaces of small dimension over
small fields and the construction of a transitive -general set of size in ,
An infinite family of -ovoids of the hyperbolic quadrics
An infinite family of -ovoids of , , admitting the group , is constructed. The main
tool is the general theory of generalized hexagons.Comment: 9 page
Intriguing sets of strongly regular graphs and their related structures
In this paper we outline a technique for constructing directed strongly regular graphs by using strongly regular graphs having a "nice" family of intriguing sets. Further, we investigate such a construction method for rank three strongly regular graphs having at most vertices. Finally, several examples of intriguing sets of polar spaces are provided
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