Abstract: The encoder/decoder system uses encoder hardware to encode data symbols and form a data code word. To decode, the system uses the same encoder hardware to determine a residue r(x), i.e. ##EQU1## where C.sub.r (x) is the retrieved code word and g(x) is the generator polynomial. If the residue is all zeros, the ECC code word is error-free and the system need not calculate the error syndrome. If the residue is non-zero, the encoder hardware is used, with various switches in different settings, to include certain multipliers in and exclude other multipliers from the further decoding operations of encoding the residue symbols to produce partial error syndromes that are the coefficients of the error syndrome polynomial.