A decoding method includes that when encoding at a sending terminal, for a m-order primitive polynomial P(x), a primitive field element in galois field GF(2m) is represented by α; a lookup table f(αj) for different power exponents of α is established, where the value of j is selected from all the integers ranging from 0 to 2m−1, with a total number of 2m; a generator polynomial G(x) is expanded to obtain a polynomial with respect to x, with coefficients being an addition or subtraction of the power exponents of α; a remainder polynomial R(x), obtained by dividing code word polynomial Q(x) by the generator polynomial G(x), is a polynomial with respect to x, with coefficients being an addition or subtraction of the power exponents of α; and the coefficients of the generator polynomial G(x) and the remainder polynomial R(x) are both calculated using data found in the lookup table f(αj).
