Yesterday I linked to an implementation (with complexity quadratic in the number of errors) I helped to create in another comment in this thread.

> constant factor using Chien's search algorithm

Chien's search is only really reasonable for small field sizes... which I think doesn't really make sense in this application, where the list is long and the missing elements are relatively few.

Fortunately in characteristic 2 it's quite straight forward and fast to just factor the polynomial using the berlekamp trace algorithm.