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# Improved upper bounds for partial spreads

## Title data

Kurz, Sascha:
Improved upper bounds for partial spreads.
2016
Event: Network Coding and Designs , 4.-8.04.2016 , Dubrovnik, Kroatien.
(Conference item: Conference , Speech )

## Project information

Project title:
Project's official titleProject's id
Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche GeometrieKU 2430/3-1

Project financing: Deutsche Forschungsgemeinschaft

## Abstract in another language

A partial $(k-1)$-spread in $PG(n-1,q)$ is a collection of $(k-1)$-dimensional subspaces with trivial intersection such that each point is covered exactly once. So far the maximum size $A_q(n,2k;k)$ of a partial $(k-1)$-spread in $PG(n-1,q)$ was known for the cases $n\equiv 0\pmod k$, $n\equiv 1\pmod k$ and $n\equiv 2\pmod k$ with the
additional requirements $q=2$ and $k=3$. We completely resolve the case $n\equiv 2\pmod k$ for the binary case $q=2$.

Theorem:
For each pair of integers $t\ge 1$ and $k\ge 4$ we have $A_2(k(t+1)+2,2k;k)=\frac{2^{k(t+1)+2}-3\cdot 2^{k}-1}{2^k-1}$.

Theorem:
For integers $t\ge 1$ and $k\ge 4$ we have $A_3(k(t+1)+2,2k;k) \le \frac{3^{k(t+1)+2}-3^2}{3^k-1}-\frac{3^2+1}{2}$.

## Further data

Item Type: Conference item (Speech) No Galois geometry; partial spreads; constant dimension codes; vector space partitions; orthogonal arrays; (s,r,μ)-nets Mathematics Subject Classification Code: 51E23 (05B15 05B40 11T71 94B25) Faculties > Faculty of Mathematics, Physics und Computer ScienceFaculties > Faculty of Mathematics, Physics und Computer Science > Department of MathematicsFaculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in EconomyFaculties Yes 500 Science > 510 Mathematics 18 Apr 2016 07:15 18 Apr 2016 07:15 https://eref.uni-bayreuth.de/id/eprint/32190