Decoding of One-Point Codes with Koetter's Algorithm

Mike O'Sullivan (San Diego State University)

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.