1. A system for correcting errors in a codeword, the system comprising: a channel that sorts reliability numbers of symbols in the codeword to create an ordered list of candidate erasure locations; and a generalized minimum distance decoder that iteratively processes the ordered list of candidate erasure locations and at least two syndromes of the codeword using a single-shot key equation solver to generate an error locator polynomial and an error evaluator polynomial, wherein the generalized minimum distance decoder processes the least reliable candidate erasure locations first within the ordered list of candidate erasure locations.