Generalized rank weights : a duality statement
Date of Issue2015
11th International Conference on Finite Fields and their Applications
School of Physical and Mathematical Sciences
We consider linear codes over some ﬁxed ﬁnite ﬁeld extension Fq m/Fq, where Fq is an arbitrary ﬁnite ﬁeld. In , Gabidulin introduced rank metric codes, by endowing linear codes over Fq m with a rank weight over Fq and studied their basic properties in analogy with linear codes and the classical Hamming distance. Inspired by the characterization of the security in wiretap II codes in terms of generalized Hamming weights by Wei , Kurihara et al. deﬁned in  some generalized rank weights and showed their relevance for secure network coding. In this paper, we derive a statement for generalized rank weights of the dual code, completely analogous to Wei’s one for generalized Hamming weights and we characterize the equality case of the rth-generalized Singleton bound for the generalized rank weights, in terms of the rank weight of the dual code.
DRNTU::Science::Physics::Atomic physics::Field theories
© 2015 American Mathematical Society. This is the author created version of a work that has been peer reviewed and accepted for publication by Contemporary Mathematics, American Mathematical Society. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://www.ams.org/books/conm/632/].