A Vector Version of the BMS Algorithm for Implementing Fast Erasure-and-Error Decoding of One-Point AG Codes

In this paper1 we propose a fast erasure-and-error decoding method for any one-point Algebraic-Geometric (AG) codes up to the Feng-Rao bound, which is a modification of the Sakata algorithm (the nD Berlekamp-Massey algorithm) and is given as a unification of our previous fast error-only decoding method and the algorithm for finding a minimal polynomial vector set of a given vector of nD arrays.

[1]  Tom Høholdt,et al.  A Fast Decoding Method of AG Codes from Miura-Kamiya Curves Cab up to Half the Feng-Rao Bound , 1995 .

[2]  Shojiro Sakata,et al.  Extension of the Berlekamp-Massey Algorithm to N Dimensions , 1990, Inf. Comput..

[3]  Shojiro Sakata,et al.  Finding a Minimal Polynomial Vector Set of a Vector of nD Arrays , 1991, AAECC.

[4]  Shojiro Sakata,et al.  Finding a Minimal Set of Linear Recurring Relations Capable of Generating a Given Finite Two-Dimensional Array , 1988, J. Symb. Comput..

[5]  Douglas A. Leonard.  Error-locator ideals for algebraic-geometric codes , 1995, IEEE Trans. Inf. Theory.

[6]  阪田 省二郎,et al.  Shift Register Synthesis on Convex Cones and Cylinders and Fast Decoding of General One-point AG Codes , 1995 .

[7]  Ruud Pellikaan,et al.  On the decoding of algebraic-geometric codes , 1995, IEEE Trans. Inf. Theory.

[8]  Tom Høholdt,et al.  Generalized Berlekamp-Massey decoding of algebraic-geometric codes up to half the Feng-Rao bound , 1994, IEEE Trans. Inf. Theory.

[9]  G. David Forney,et al.  On decoding BCH codes , 1965, IEEE Trans. Inf. Theory.

[10]  A.N. Skorobogatov,et al.  On the decoding of algebraic-geometric codes , 1990, IEEE Trans. Inf. Theory.

[11]  T. R. N. Rao,et al.  Decoding algebraic-geometric codes up to the designed minimum distance , 1993, IEEE Trans. Inf. Theory.

[12]  Masazumi Kurihara,et al.  A systolic array architecture for implementing a fast parallel decoding algorithm of one-point AG codes , 1997, Proceedings of IEEE International Symposium on Information Theory.

[13]  Tom Høholdt,et al.  Fast decoding of algebraic-geometric codes up to the designed minimum distance , 1995, IEEE Trans. Inf. Theory.