Fast decoding of algebraic-geometric codes up to the designed minimum distance

Authors:
S. Sakata;J. Justesen;Y. Madelung;H. E. Jensen;T. Hoholdt
Affiliations:
Dept. of Comput. Sci. & Inf. Math., Univ. of Electro-Commun., Tokyo;-;-;-;-
Venue:
IEEE Transactions on Information Theory - Part 1
Year:
2006

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Computer algebra handbook
Asymmetric Code-Theoretical Schemes Constructed with the Use of Algebraic Geometric Codes

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Abstract

We present a decoding algorithm for algebraic-geometric codes from regular plane curves, in particular the Hermitian curve, which corrects all error patterns of weight less than d*/2 with low complexity. The algorithm is based on the majority scheme of Feng and Rao (1993) and uses a modified version of Sakata's (1988) generalization of the Berlekamp-Massey algorithm