Coding for data storage via matroid theory

Dr. Ragnar Freij-Hollanti

TUM

Abstract:

A lot of recent research on coding theory, especially motivated by data storage applications, has focused on the locality and repairability of storage codes. Codes designed with such properties in mind are for example locally repairable codes, codes with availability, batch codes, etc. We argue that locality and repairability can be naturally discribed in terms of matroids, and more specifically in terms of their so-called lattices of cyclic flats.

In this talk, we will gently introduce matroids, with a special focus on their connections to coding theory. We will also discuss qualitative obstructions to representability over small fields, which in turn gives criteria for possible locality properties of linear storage codes.

Biography:

Dr Ragnar Freij-Hollanti obtained his PhD in Mathematics from Chalmers University of Technology in Sweden in 2012. During 2012-2017, he was a postdoctoral fellow at Aalto University in Finland. During 2017-2018, he is a postdoctoral fellow at TU Munich, in the research group of Professor Wachter-Zeh. His research revolves around algebraic and combinatorial methods in coding theory and discrete geometry, in particular with applications to data storage and communications.