Title: Semifields, Maximum Rank Distance codes and related geometric structures
Speaker: Professor Rocco Trombetti (University of Naples Federico II)
Time: 7:00-8:00pm, Sep 5, 2017
Venue: 200-9, Sir Run-Run Shaw Business Building, Yuquan Campus
In the last decade maximum rank distance codes gained great interest from the part of Finite Geometers. This mainly because of their application in the context of random network coding, and because of their connections with many interesting structures in finite geometry, such as semifields and linear sets.
As a consequence of this renewed interest in the topic, several new constructions appeared in recent years, and sometime these techniques also led to new semifields.
In general it is difficult to tell whether two rank metric codes with the same parameters are equivalent or not. For semifields, there are some classical invariants i.e., the sizes of their so called nuclei, as well as the geometric structure of their associated linear set. These invariants reveled to be quite useful in telling the equivalence between two semifields, and many classification results on semifields are also based on certain assumptions on them.
In this talk we will survey some of these classification results, and address the problem of defining above mentioned structures for other rank metric codes.