Abstract: A method and apparatus for encoding and decoding linear block codes while using limited working storage is disclosed. For decoding, the error syndromes are calculated incrementally as each encoded symbol is received. That is, as each symbol, ri of the code word is received, the received symbol, ri is multiplied by the entries in the “ith” column of a decoding matrix, resulting in intermediate syndrome components. The intermediate syndrome components are added to the appropriate entry in a syndrome vector. Once all symbols ri are received, the syndrome vector contains the error syndromes si for the received code word.