A Reed-Solomon decoder in which the coefficients of an error locator polynomial ($g(s)_u) are calculated on the basis of the values of 2t syndromes (S_i) is disclosed. A calculation cell (64_u) provided for each coefficient comprises two multiplier circuits, two registers for storing a coefficient of the locator polynomial and the coefficient of a related intermediate polynomial, and means for updating the coefficient values in the respective registers. The key equation is solved in 2t iterations that each comprise a first phase for calculating a prediction deviation ($g(D)_k) and a second phase for updating the coefficients.