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.
Originalsprog | Engelsk |
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Titel | Applied Algebra, Algebraic Algorithms and Error-Correcting Codes |
Redaktører | Marc Fossorier, Hideki Imai, Shu Lin, Alain Poli |
Vol/bind | 3857 |
Forlag | IEEE Computer Society Press |
Publikationsdato | 2006 |
Sider | 295-306 |
ISBN (Trykt) | 3540314237 |
DOI | |
Status | Udgivet - 2006 |
Begivenhed | On the Feng-Rao bound for generalized hamming weights - Varighed: 19 maj 2010 → … |
Konference
Konference | On the Feng-Rao bound for generalized hamming weights |
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Periode | 19/05/2010 → … |