| Autor: |
Fossorier, Marc, Imai, Hideki, Lin, Shu, Poli, Alain, Geil, Olav, Thommesen, Christian |
| Zdroj: |
Applied Algebra, Algebraic Algorithms & Error-Correcting Codes; 2006, p295-306, 12p |
| Abstrakt: |
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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Supplemental Index |
| Externí odkaz: |
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