Decoding of One-Point Codes with Koetter's Algorithm

In the early 1980's Goppa introduced the use of error correcting codes constructed from algebraic curves. These codes generalize Reed-Solomon codes, which are widely used in communications systems. Over the next two decades efficient algorithms were developed for decoding codes from curves by generalizing the Berlekamp-Massey algorithm for decoding Reed-Solomon codes. I will present the Berlekamp-Massey algorithm and then show a generalization to curves based on the work of Ralf Koetter.