On the Feng-Rao bound for generalized hamming weights

Hans Olav Geil, Christian Thommesen

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

7 Citations (Scopus)

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
Title of host publicationApplied Algebra, Algebraic Algorithms and Error-Correcting Codes
EditorsMarc Fossorier, Hideki Imai, Shu Lin, Alain Poli
Volume3857
PublisherIEEE Computer Society Press
Publication date2006
Pages295-306
ISBN (Print)3540314237
DOIs
Publication statusPublished - 2006
EventOn the Feng-Rao bound for generalized hamming weights -
Duration: 19 May 2010 → …

Conference

ConferenceOn the Feng-Rao bound for generalized hamming weights
Period19/05/2010 → …

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