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List decoding algorithms based on Gröbner bases for general one-point AG codes

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3 Author(s)
Geil, O. ; Dept. of Math. Sci., Aalborg Univ., Aalborg, Denmark ; Matsumoto, R. ; Ruano, D.

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan [15] based on Gröbner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander [4]. By using the same principle, we also generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cab curves proposed by Lee, Bras-Amorós and O'Sullivan [14] to general one-point AG codes, without any assumption. Finally we extend the latter 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, and remove the unnecessary computational steps so that it can run faster.

Published in:

Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on

Date of Conference:

1-6 July 2012