A Reed-Solomon, RS, error correction encoding and decoding method, wherein, when encoding at a sending terminal, the following holds: • code words of information data are represented by K l, • code words of redundant codes are represented by T n, • the order of primitive polynomial P(x) is m, • a generator polynomial in GF(2 m) is G(x), and • an error correction code is represented by (c, k, t), wherein c is the total length of the information data and the redundant code, k is the length of the information data, and t is the length of the redundant code, then • the code word polynomial Q(x) can be represented as Q x = ∑ l = t t + k − 1 K l ⋅ x l + ∑ n = 0 t − 1 T n ⋅ x n; • a root of the m-order primitive polynomial P(x) is a primitive field element in GF (2 m), and the primitive field element is represented by α, thus the generator polynomial G(x) can be represented as G x = ∏ i = 1 t x − α i; the method including the steps of: • establishing one lookup table f(α j) including different powers,α j, of α, for j = 0, 1,..., 2m-1, i.e. f(α j) = { α 0, α 1,..., α (2m-1)}; • expanding the generator polynomial G(x) to obtain a polynomial with respect to x, wherein the coefficients of the generator polynomial G(x) are the addition or subtraction of the powers of α; wherein numerical values of the different powers of α are found out through the lookup table f(α j) and the coefficients of the generator polynomial G(x) are calculated; and wherein it is assumed that the code words T n of the redundant codes are all 0, then a code word polynomial Q x = ∑ l = t t + k − 1 K l ⋅ x l is obtained; • dividing the code word polynomial Q(x) by the generator polynomial G(x) to obtain a remainder polynomial R x = ∑ n = 0 t − 1 T n x n, wherein the coefficients T n of R(x) are the addition or subtraction of the powers of α; and wherein numerical values of the powers of α are found out through the lookup table f(α j), and the coefficients T n of the remainder polynomial R(x) are calculated. • code words of information data are represented by K l, • code words of redundant codes are represented by T n, • the order of primitive polynomial P(x) is m, • a generator polynomial in GF(2 m) is G(x), and • an error correction code is represented by (c, k, t), wherein c is the total length of the information data and the redundant code, k is the length of the information data, and t is the length of the redundant code, then • the code word polynomial Q(x) can be represented as Q x = ∑ l = t t + k − 1 K l ⋅ x l + ∑ n = 0 t − 1 T n ⋅ x n; • a root of the m-order primitive polynomial P(x) is a primitive field element in GF (2 m), and the primitive field element is represented by α, thus the generator polynomial G(x) can be represented as G x = ∏ i = 1 t x − α i; • the code word polynomial Q(x) can be represented as Q x = ∑ l = t t + k − 1 K l ⋅ x l + ∑ n = 0 t − 1 T n ⋅ x n; • a root of the m-order primitive polynomial P(x) is a primitive field element in GF (2 m), and the primitive field element is represented by α, thus the generator polynomial G(x) can be represented as G x = ∏ i = 1 t x − α i; the method including the steps of: • establishing one lookup table f(α j) including different powers,α j, of α, for j = 0, 1,..., 2m-1, i.e. f(α j) = { α 0, α 1,..., α (2m-1)}; • expanding the generator polynomial G(x) to obtain a polynomial with respect to x, wherein the coefficients of the generator polynomial G(x) are the addition or subtraction of the powers of α; wherein numerical values of the different powers of α are found out through the lookup table f(α j) and the coefficients of the generator polynomial G(x) are calculated; and wherein it is assumed that the code words T n of the redundant codes are all 0, then a code word polynomial Q x = ∑ l = t t + k − 1 K l ⋅ x l is obtained; • dividing the code word polynomial Q(x) by the generator polynomial G(x) to obtain a remainder polynomial R x = ∑ n = 0 t − 1 T n x n, wherein the coefficients T n of R(x) are the addition or subtraction of the powers of α; and wherein numerical values of the powers of α are found out through the lookup table f(α j), and the coefficients T n of the remainder polynomial R(x) are calculated. • establishing one lookup table f(α j) including different powers,α j, of α, for j = 0, 1,..., 2m-1, i.e. f(α j) = { α 0, α 1,..., α (2m-1)}; • expanding the generator polynomial G(x) to obtain a polynomial with respect to x, wherein the coefficients of the generator polynomial G(x) are the addition or subtraction of the powers of α; wherein numerical values of the different powers of α are found out through the lookup table f(α j) and the coefficients of the generator polynomial G(x) are calculated; and wherein it is assumed that the code words T n of the redundant codes are all 0, then a code word polynomial Q x = ∑ l = t t + k − 1 K l ⋅ x l is obtained; • dividing the code word polynomial Q(x) by the generator polynomial G(x) to obtain a remainder polynomial R x = ∑ n = 0 t − 1 T n x n, wherein the coefficients T n of R(x) are the addition or subtraction of the powers of α; and wherein numerical values of the powers of α are found out through the lookup table f(α j), and the coefficients T n of the remainder polynomial R(x) are calculated.