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

Authors:
S. Sakata;J. Justesen;Y. Madelung;H. E. Jensen;T. Hø/holdt
Affiliations:
Department of Computer Science and Information Mathematics, The University of Electro-Communications, Chofu-shi. Tokyo 182, Japan/ The Institute of Circuit Theory and Telecommunication, Technical ...;Department of Computer Science and Information Mathematics, The University of Electro-Communications, Chofu-shi. Tokyo 182, Japan/ The Institute of Circuit Theory and Telecommunication, Technical ...;Department of Computer Science and Information Mathematics, The University of Electro-Communications, Chofu-shi. Tokyo 182, Japan/ The Institute of Circuit Theory and Telecommunication, Technical ...;Department of Computer Science and Information Mathematics, The University of Electro-Communications, Chofu-shi. Tokyo 182, Japan/ The Institute of Circuit Theory and Telecommunication, Technical ...;Department of Computer Science and Information Mathematics, The University of Electro-Communications, Chofu-shi. Tokyo 182, Japan/ The Institute of Circuit Theory and Telecommunication, Technical ...
Venue:
Finite Fields and Their Applications
Year:
1995

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Abstract

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 C"a"b. 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 d"F"R 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.