Title data
Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Upper bounds for partial spreads from divisible codes.
2017
Event: The 13th International Conference on Finite Fields and their Applications
, 04.10.06.2017
, Gaeta, Italy.
(Conference item: Conference
,
Speech
)
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Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
A partial tspread in GF(q)^n is a collection of tdimensional subspaces with trivial intersection such that
each nonzero vector is covered at most once. How many tdimensional subspaces can be packed into GF(q)^n , i.e., what is the maximum cardinality of a partial tspread? 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^{t1}divisible linear block code. This allows to apply
the linear programming method, i.e., to utilize the socalled 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 stateoftheart.
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; divisible 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 08:16 
Last Modified:  02 May 2017 08:16 
URI:  https://eref.unibayreuth.de/id/eprint/36897 