Large Structures Seminar: Ragnar Freij

Cooperative locally repairable codes have recently gathered wide interest, both for their applications in large scale distributed storage systems, and for their purely mathematical properties. In this talk, we consider a (to our knowledge) new generalization of locally repairable codes, where the repair can be performed on several different scales, further enhancing the robustness of a storage system.

We analyze locally repairable codes from the perspective of the strong connection between linear codes and matroids, and more generally between arbitrary codes and polymatroids. We prove that a certain type of Singleton-like bounds are equivalent for matroids and codes, and apply well known techniques to calculate Tutte and rank polynomials to determine the weight enumeration polynomials on locally repairable codes.