A system for hardware error-correcting code (ECC) detection or correction of a received codeword from an original codeword includes 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 includes 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.