Computer Science – Information Theory
Scientific paper
2012-03-28
Computer Science
Information Theory
IEEEtran.cls, 13 pages, 3 tables. This is a journal paper version of Sec. 4 of the previous conference paper arXiv:1201.6248v4
Scientific paper
We generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya $C_{ab}$ curves proposed by Lee, Bras-Amor\'os and O'Sullivan 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 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.
Geil Olav
Matsumoto Ryutaroh
Ruano Diego
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