On the Feng-Rao bound for generalized Hamming weights

Olav Geil, Christian Thommesen

Research output: Book/ReportReportResearch

330 Downloads (Pure)

Abstract

The Feng-Rao bound gives good estimates of the minimum distance of a large class of codes. In this work we are concerned with the problem of how to extend the Feng-Rao bound so that it deals with all the generalized Hamming weights. The problem was solved by Heijnen and Pellikaan in [7] for a large family of codes that includes the duals of one-point geometric Goppa codes and the q-ary Reed-Muller codes, but not the Feng-Rao improved such ones. We show that Heijnen and Pellikaan’s results holds for the more general class of codes for which the traditional Feng-Rao bound can be applied. We also establish the connection to the Shibuya-Sakaniwa bound for generalized Hamming weights ([15], [16], [17], [18], [19] and [20]). More precisely we show that the Shibuya-Sakaniwa bound is a consequence of the extended Feng-Rao bound. In particular the extended Feng-Rao bound gives always at least as good estimates as does the Shibuya-Sakaniwa bound.
Original languageEnglish
Number of pages12
Publication statusPublished - 2005
SeriesResearch Report Series
NumberR-2005-33
ISSN1399-2503

Fingerprint Dive into the research topics of 'On the Feng-Rao bound for generalized Hamming weights'. Together they form a unique fingerprint.

Cite this