Some results on the Sudan algorithm [for decoding Reed-Solomon codes]

Sudan (see Journal of Complexity, vol.13, no.1, p.180-93, 1997) published a new algorithm that can decode low rate Reed-Solomon codes beyond their packing radii; he also gave an expression for the error-correcting capability and an upper bound on the number of outputs. We give a simpler derivation which leads to simpler expressions for the error-correcting capability and a bound on the number of outputs of the algorithm. We also observe that the Sudan algorithm provides some information on the distance structure of low rate Reed-Solomon codes at distance larger than the packing radii. Furthermore, our approach is more intuitive, for example, our expression of the error-correcting capability naturally reduces to the packing radii for high-rate codes.