A Fast Decoding Method of AG Codes from Miura-Kamiya Curves Cab up to Half the Feng-Rao Bound

We present a fast version of the Feng-Rao algorithm for decoding of one-point algebraic-geometric (AG) codes derived from the curves which Miura and Kamiya classified as Cab. Our algorithm performs the Feng-Rao algorithm efficiently by using the Sakata algorithm, i.e., the 2D Berlekamp-Massey algorithm. One can decode the one-point AG codes up to half of the Feng-Rao bound dFR which is greater than or equal to the designed distance d*. We have proven the validity and the performance of our algarithm in the framework of our own theory, depending little on algebraic geometry.