Title data
Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Partial Spreads and Vector Space Partitions.
In: Greferath, Marcus ; Pavčević, Mario Osvin ; Silberstein, Natalia ; VázquezCastro, María Ángeles
(ed.):
Network Coding and Subspace Designs. 
Cham
: Springer
,
2018
.  pp. 131170
.  (Signals and Communication Technology
)
ISBN 9783319702926
DOI: https://doi.org/10.1007/9783319702933_7
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Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
Constantdimension codes with the maximum possible minimum distance have been studied under the name of partial spreads in Finite Geometry for several decades. Not surprisingly, for this subclass typically the sharpest bounds on the maximal code size are known. The seminal works of Beutelspacher and Drake & Freeman on partial spreads date back to 1975 and 1979, respectively. From then until recently, there was almost no progress besides some computerbased constructions and classifications. It turns out that vector space partitions provide the appropriate theoretical framework and can be used to improve the longstanding bounds in quite a few cases. Here, we provide a historic account on partial spreads and an interpretation of the classical results from a modern perspective. To this end, we introduce all required methods from the theory of vector space partitions and Finite Geometry in a tutorial style. We guide the reader to the current frontiers of research in that field, including a detailed description of the recent improvements.