RT info:eu-repo/semantics/article
T1 Feng-Rao decoding of primary codes
A1 Geil, Olav
A1 Matsumoto, Ryutaroh
A1 Ruano Benito, Diego
AB 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 towhat is guaranteed by their bound. The exposition in Matsumoto-Miura requires the useof 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.
YR 2013
FD 2013
LK http://uvadoc.uva.es/handle/10324/31743
UL http://uvadoc.uva.es/handle/10324/31743
LA eng
NO Finite Fields and their Applications. Volume 23, pages 35-52 (2013)
NO Producción Científica
DS UVaDOC
RD 06-ago-2024