In this article, 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.

The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt (see ibid., vol. 41, p. 1762-8, Nov. 1995) corrects all error patterns of weight less than half the Feng-Rao minimum distance. In this correspondence we analyze the performance of the algorithm for heavier error patterns. It turns out that in the typical case, where the error points are "independent", one can prove that the algorithm always fails, that is gives a wrong or no answer, except for high rates where it does much better than expected. This explains the simulation results presented by O'Sullivan at the IEEE Int. Symp. Information Theory, Ulm, Germany (1997). We also show that for dependent errors the algorithm almost always corrects these.