The present invention provides a RS error correction decoding method. In the method, when encoding at a sending terminal, for a m-order primitive polynomial P(x), a primitive field element in galois field GF(2 m ) is represented by ±; a lookup table f(± j ) for different power exponents of ± 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 ±; 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 ±; 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(± j ). With the RS error correction decoding method, system memory is
