Performance analysis of a decoding algorithm for algebraic-geometry codes

The fast decoding algorithm for one point algebraic geometry codes of Sakata, Elbrnd Jensen and Hholdt corrects all error patterns of weight less than half the Feng-Rao minimum distance. In this paper we analyse 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 1997 ISIT. We also show that for dependent errors the algorithm almost always corrects these. Keywords Decoding, Algebraic Geometry Codes, Performance. I. Introduction. O NE of the main problems in decoding is to analyse the performance of a decoding algorithm when the error pattern has weight greater than half the minimum distance of the code. Recently M. O'Sullivan [1] presented simulation results for some Hermitian Codes and..