MacWilliams Identity for Codes with the Rank Metric

Gadouleau, Maximilien; Yan, Zhiyuan

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
• Electronic ISSN: 1687-1499
• Publisher: SpringerOpen
• Peer Reviewed: Peer Reviewed
• Volume: 2008
• Article Number: 754021
• DOI: https://doi.org/10.1155/2008/754021
• Public URL: https://durham-repository.worktribe.com/output/1531320