1 Department of Mathematical Sciences, The Faculty of Engineering and Science, Aalborg University, VBN2 The Faculty of Engineering and Science, Aalborg University, VBN
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  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 (, , , ,  and ). 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.
Applied Algebra, Algebraic Algorithms and Error-correcting Codes, 2006, p. 295-306
Main Research Area:
On the Feng-Rao bound for generalized hamming weights, 2006