A method for generating syndromes for a data block is disclosed. The method generally includes the steps of (A) calculating a plurality of row syndromes and a plurality of column syndromes for the data block arranged as a Reed-Solomon product code, (B) storing only the row syndromes and the column syndromes in a local memory, (C) in an alternating sequence (i)(a) decoding the column syndromes to generate column correction results and (b) updating the row syndromes in response to the column correction results and (ii)(a) decoding the row syndromes to generate row correction results and (b) updating the column syndromes in response to the row correction results.