List Decoding Algorithm based on Voting in Gröbner Bases for General One-Point AG Codes

We generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cab curves proposed by Lee, Bras-Amorós, and O’Sullivan [31] to general one-point AG codes, without any assumption. We also extend their unique decoding algorithm to list decoding, modify it so that it can be used with the Feng-Rao improved code construction, prove equality between its error correcting capability and half the minimum distance lower bound by Andersen and Geil [3] that has not been done in the original proposal except for one-point Hermitian codes, remove the unnecessary computational steps so that it can run faster, and analyze its computational complexity in terms of multiplications and divisions in the finite field. As a unique decoding algorithm, the proposed one is as fast as the BMS algorithm for one-point Hermitian codes, and as a list decoding algorithm it is much faster than the algorithm by Beelen and Brander [5].