On the Feng-Rao bound for generalized hamming weights

Hans Olav Geil, Christian Thommesen

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

7 Citationer (Scopus)


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.
TitelApplied Algebra, Algebraic Algorithms and Error-Correcting Codes
RedaktørerMarc Fossorier, Hideki Imai, Shu Lin, Alain Poli
ForlagIEEE Computer Society Press
ISBN (Trykt)3540314237
StatusUdgivet - 2006
BegivenhedOn the Feng-Rao bound for generalized hamming weights -
Varighed: 19 maj 2010 → …


KonferenceOn the Feng-Rao bound for generalized hamming weights
Periode19/05/2010 → …


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