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Abstract. We present an efficient implementation of Sudan's algorithm for list decoding Hermitian codes beyond half the minimum distance. The main ingredients are an explicit method to calculate so-called increasing zero bases, an efficient interpolation algorithm for finding the Qpolynomial, and a reduction of the problem of factoring the Q-polynomial to the problem of factoring a univariate polynomial over a large finite field.
Abstract-In this correspondence, Sudan's algorithm is modified into an efficient method to list-decode a class of codes which can be seen as a generalization of Reed-Solomon codes. The algorithm is specialized into a very efficient method for unique decoding. The code construction can be generalized based on algebraic-geometry codes and the decoding algorithms are generalized accordingly. Comparisons with Reed-Solomon and Hermitian codes are made.
-We analyse t h e k:nown d e c o d i n g alg e r i t h m s for algebraic g e o m e t r y codes in t h e case w h e r e t h e n u m b e r of e r r o r s is [ (~F R -l)/Z] + 1, w h e r e d p~ is t h e Feng-Rao distance.
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