The invention relates to an encoding method for encoding a codeword to obtain a parity code. The code is embedded in the codeword and divides the codeword to have intermediate symbol locations between a first and a second set of data symbols. Each data symbol forms a coefficient. The first and the second set of data symbols and the parity code respectively form a first polynomial (M1(x)), a second polynomial (M2(x)), and a parity code polynomial (R(x)). The method comprises: first, designing a first code generator polynomial (G1(x)); next, dividing M1(x)x4 by G1(x) to obtain a first remainder polynomial (R1(x)); next, generating a second code generator polynomial (G2(x)) from G1(x); next, generating a third polynomial (M3(x)); next, dividing M3(x)x4 by G2(x) to obtain a second remainder polynomial (R2(x)); next, performing an adding procedure to R1(x) and R2(x) to obtain R(x); finally, obtaining the parity code from each coefficient of R(x).