MacWilliams Identity for Codes with the Rank Metric
Information Theory
2007-11-28 v3 math.IT
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.
Keywords
Cite
@article{arxiv.0706.1751,
title = {MacWilliams Identity for Codes with the Rank Metric},
author = {Maximilien Gadouleau and Zhiyuan Yan},
journal= {arXiv preprint arXiv:0706.1751},
year = {2007}
}