MacWilliams Identity for Codes with the Rank Metric

Details MacWilliams Identity for Codes with the Rank Metric MacWilliams Identity for Codes with the Rank Metric

2007-06-12

arxiv.org/abs/0706.1751v3

Computer Science

Information Theory

25 pages, submitted to EURASIP Journal on Wireless Communications

Scientific paper

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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