Decoding algebraic geometric codes

We present a new algorithm for decoding AG-codes significantly beyond the error-correction bound. Specifically, given a word y whose distance to the AG-code is at most e, where e is a parameter depending on the block length and the dimension of the code, our algorithm produces all codewords that have distance ⩽e from y. We also discuss modifications of our general algorithm and show how to obtain similar algorithms for binary codes using concatenated codes