MacWilliams Identity for Codes with the Rank Metric
Maximilien Gadouleau, Zhiyuan Yan
TL;DR
This paper derives a new form of the MacWilliams identity specifically for linear codes with the rank metric, expanding the theoretical tools available for analyzing such codes.
Contribution
The paper introduces a novel MacWilliams identity for rank metric codes, differing from Delsarte's form, and derives related identities similar to those for Hamming metric codes.
Findings
New MacWilliams identity for rank metric codes
Derived identities parallel Hamming metric binomial and moment identities
Provides theoretical foundation for analyzing rank metric code distributions
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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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Advanced Wireless Communication Techniques