  Let $q$ be a prime power and $\mathbb F_q$ be the finite field of size $q$.
In this paper we provide a Galois theoretical framework that allows to produce
good polynomials for the Tamo and Barg construction of optimal locally
recoverable codes (LRC). Using our approach we construct new good polynomials
and then optimal LRCs with new parameters. The existing theory of good
polynomials fits entirely in our new framework. The key advantage of our method
is that we do not need to rely on arithmetic properties of the pair $(q,r)$,
where $r$ is the locality of the code.
