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MacWilliams Identity for Codes with the Rank Metric

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.

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Correspondence to Maximilien Gadouleau.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Gadouleau, M., Yan, Z. MacWilliams Identity for Codes with the Rank Metric. J Wireless Com Network 2008, 754021 (2008). https://doi.org/10.1155/2008/754021

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Keywords

  • Information System
  • System Application
  • Weight Distribution
  • Linear Code
  • Full Article