A method for computing parity characters for a codeword of a cyclic code successively generates a sum of an output value and a respective message character of a first message section adjacent to parity characters within a first block. The method then successively multiplies a respective sum by corresponding coefficients of a generator polynomial to generate at least one product. The method further successively multiplies a respective message character of every message section other than the first message section by coefficients of a corresponding shift polynomial to generate a plurality of products, before finally, successively summing corresponding products to generate the output value.