unit 16 outputs decoded data and can include a display for displaying image data a speaker for outputting decoded voice data and the like a decoding procedure of a reed solomon rs code c can be used in decoding processing unit 14 in this decoding procedure the code word received at input unit 12 is represented by a k dimensional reed solomon code c corresponding to a set of points x x m in a galois field gf q represented by the set of all vectors of the form f x 1 f x m where f ranges over all polynomials of degree less than k with coefficients in gf q the decoding procedure is a list decoder of distance e for the rs code c which takes as input any m dimensional vector y 1 y m of a received word with coefficients in gf q and outputs all vectors in rs code c which differ in at most e positions from y 1 y m a list decoder can be designed given target list size l and the vector y 1 y m from a polynomial h x y h 1 x h 2 x y h l 1 x y.