2026-05-05T19:59:26Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/317432024-12-18T15:53:22Zcom_10324_32197com_10324_952com_10324_894com_10324_1129com_10324_931col_10324_32199col_10324_1193

Feng-Rao decoding of primary codes Geil, Olav Matsumoto, Ryutaroh Ruano Benito, Diego We show that the Feng-Rao bound for dual codes and a similar bound by Andersen and Geil for primary codes are consequences of each other. This implies that the Feng-Rao decoding algorithm can be applied to decode primary codes up to half their designed minimum distance. The technique applies to any linear code for which information on well-behaving pairs is available. Consequently we are able to decode efficiently a large class of codes for which no non-trivial decoding algorithm was previously known. Among those are important families of multivariate polynomial codes. Matsumoto and Miura derived from the Feng-Rao bound a bound for primary one-point algebraic geometric codes and showed how to decode up to what is guaranteed by their bound. The exposition in Matsumoto-Miura requires the use of differentials which was not needed in Andersen-Geil. Nevertheless we demonstrate a very strong connection between Matsumoto and Miura's bound and Andersen and Geil's bound when applied to primary one-point algebraic geometric codes. 2018-09-25T11:07:23Z 2018-09-25T11:07:23Z 2018-09-25T11:07:23Z 2013 info:eu-repo/semantics/article Finite Fields and their Applications. Volume 23, pages 35-52 (2013) http://uvadoc.uva.es/handle/10324/31743 10.1016/j.ffa.2013.03.005 eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 International