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Upper bounds for partial spreads

Title data

Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Upper bounds for partial spreads.
2017
Event: Computeralgebra-Tagung 2017 , 04.-06.05.2017 , Kassel, Deutschland.
(Conference item: Conference , Speech )

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Project information

Project title:
Project's official titleProject's id
Ganzzahlige Optimierungsmodelle für Subspace Codes und endliche GeometrieNo information

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

A partial t-spread in GF(q)^n is a collection of t-dimensional subspaces with trivial intersection such that
each non-zero vector is covered at most once. How many t-dimensional subspaces can be packed into GF(q)^n , i.e., what is the maximum cardinality of a partial t-spread? An upper bound, given by Drake and Freeman, survived almost forty years without any improvement. At the end of 2015, the upper bounds started to crumble. Here, the theoretical foundation is provided by the fact that the uncovered points, called holes in this context, form a projective q^{t-1}-divisible linear block code. This allows to apply
the linear programming method, i.e., to utilize the so-called MacWilliams identities and the positivity of the coefficients of the weight enumerator of the corresponding dual code. In this talk we will exhibit how this well known approach from coding theory can used to obtain analytical bounds on the maximum size of partial $t$-spreads that form the present state-of-the-art.

Further data

Item Type: Conference item (Speech)
Refereed: No
Additional notes: Speaker: Sascha Kurz
Keywords: Finite geometry; projective geometry; partial spreads; constant dimension subspace codes
Subject classification: Mathematics Subject Classification Code: 51E23 (05B15 05B40 11T71 94B25)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 02 May 2017 08:13
Last Modified: 02 May 2017 08:13
URI: https://eref.uni-bayreuth.de/id/eprint/36896