Partial spreads and vector space partitions

Titelangaben

Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha:
Partial spreads and vector space partitions.
Bayreuth , 2016 . - 21 S.

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Abstract

Constant dimension codes with the maximum possible minimum distance have been studied under the name of partial spreads in finite geometry for several decades. It is no surprise that the sharpest bounds on the maximal code sizes are typically known for this subclass. The seminal works of Andr\'e, Segre, Beutelspacher, and Drake & Freeman date back to 1954, 1964, 1975, and 1979, respectively. Until recently, there was almost no progress besides some computer based constructions and classifications. It turns out that vector space partitions provide the appropriate theoretical framework, Here, we provide an historic account and an interpretation of the classical results from a modern point of view. 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.