MacWilliams Identity for Codes with the Rank Metric

Gadouleau, Maximilien; Yan, Zhiyuan

doi:10.1155/2008/754021

MacWilliams Identity for Codes with the Rank Metric

Gadouleau, Maximilien; Yan, Zhiyuan

Authors

Dr Maximilien Gadouleau m.r.gadouleau@durham.ac.uk
Associate Professor

Zhiyuan Yan

Abstract

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.

Citation

Gadouleau, M., & Yan, Z. (2008). MacWilliams Identity for Codes with the Rank Metric. EURASIP Journal on Wireless Communications and Networking, 2008, Article 754021. https://doi.org/10.1155/2008/754021

Journal Article Type	Article
Acceptance Date	Mar 3, 2008
Publication Date	Mar 13, 2008
Deposit Date	Jan 13, 2012
Publicly Available Date	Oct 29, 2015
Journal	EURASIP journal on wireless communications and networking.
Print ISSN	1687-1472
Publisher	SpringerOpen
Peer Reviewed	Peer Reviewed
Volume	2008
Article Number	754021
DOI	https://doi.org/10.1155/2008/754021

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Copyright Statement
© 2008 The Author(s). 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.