Abstract: An error correction system generates a residue for data symbols encoded in accordance with an (n,k) code which has a distance "d" and a generator polynomial g(x). If the residue contains fewer than "T" non-zero symbols, where T<d/2, the data symbols are assumed to be error free. If there are T or more non-zero symbols, the data symbols are assumed to contain errors and the residue symbols are manipulated to correct the errors, if possible. The residue symbols are thus encoded using an encoder constructed in accordance with the generator polynomial g(x) by loading the residue symbols and shifting the encoder "m" times, where m is a factor of k. The number of non-zero symbols are then counted. If there are fewer than T non-zero symbols in the encoded residue, the encoded symbols are combined with the corresponding symbols in the code word. Thus the first encoded residue symbol is combined with the m.sup.th code word symbol, the second residue symbol is combined with the m+1.sup.