Open Access

MacWilliams Identity for Codes with the Rank Metric

EURASIP Journal on Wireless Communications and Networking20082008:754021

Received: 10 November 2007

Accepted: 3 March 2008

Published: 13 March 2008


The MacWilliams identity, which relates the weight distribution of a code to the weight distribution of its dual code, is useful in determining the weight distribution of codes. In this paper, we derive the MacWilliams identity for linear codes with the rank metric, and our identity has a different form than that by Delsarte. Using our MacWilliams identity, we also derive related identities for rank metric codes. These identities parallel the binomial and power moment identities derived for codes with the Hamming metric.

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Authors’ Affiliations

Department of Electrical and Computer Engineering, Lehigh University


© M. Gadouleau and Z. Yan. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.