Rank-Metric Codes: Theory and Applications
Abstract: The study of rank-metric codes can be traced back to Delsarte, who originally introduced them for a purely combinatorial interest. It is only in 2008 that these codes raised the interest of coding theorist, due to their application in network coding proposed by Silva-Koetter-Kschischang. Since then, the theory of rank-metric codes has exponentially grown, bridging researchers in mathematics, engineering and computer science.
In this talk, I will present an overview of the mathematical theory of rank-metric codes. I will start from the motivation, describing their use in network coding. I will then discuss the most interesting algebraic and geometric features of rank-metric codes, from classical results to recent research developments.