In this talk I will explain how to use Galois theory to build optimal locally recoverable codes (LRC) over finite fields. The main ingredients of the construction are the Chebotarev Density theorem and the Tamo-Barg construction of optimal LRCs. More specifically, we show that constructing optimal LRCs of large dimension and length is equivalent to the problem of finding extensions of global function fields that have small Galois closure, and have a specific form.
org: CAPUANO Laura