Systems and methods are provided for implementing list decoding in a Reed-Solomon (RS) error-correction system. A detector can provide a decision-codeword from a channel and can also provide soft-information for the decision-codeword. The soft-information can be organized into an order of combinations of error events for list decoding. An RS decoder can employ a list decoder that uses a pipelined list decoder architecture. The list decoder can include one or more syndrome modification circuits that can compute syndromes in parallel. A long division circuit can include multiple units that operate to compute multiple quotient polynomial coefficients in parallel. The list decoder can employ iterative decoding and a validity test to generate error indicators. The iterative decoding and validity test can use the lower syndromes.