Sliding window list decoder for error correcting codes

A system for hardware error-correcting code (ECC) detection or correction of a received codeword from an original codeword, the system comprising:

• an error-detecting circuit configured to process a selection of symbols of the received codeword using a set of factors, the original codeword being recomputable from a corresponding said selection of symbols of the original codeword using the set of factors, the error-detecting circuit comprising:
• a hardware multiplier and accumulator configured to use the set of factors and the selection of symbols of the received codeword to recompute remaining symbols of the original codeword;
• and
• a hardware comparator configured to compare the recomputed remaining symbols of the original codeword with corresponding said remaining symbols of the received codeword and to output first results of this comparison,
• wherein the error-detecting circuit comprises a plurality of error-detecting circuits each configured to process a different said selection of symbols of the received codeword using a different said set of factors,
• wherein the hardware comparator is further configured to compare the recomputed remaining symbols of the original codeword with the remaining symbols of the received codeword by counting a first number of the recomputed remaining symbols of the original codeword that equal respective ones of the remaining symbols of the received codeword, and
• wherein the first results comprise the first number.