English

Properties of Rank Metric Codes

Information Theory 2007-07-13 v3 math.IT

Abstract

This paper investigates general properties of codes with the rank metric. We first investigate asymptotic packing properties of rank metric codes. Then, we study sphere covering properties of rank metric codes, derive bounds on their parameters, and investigate their asymptotic covering properties. Finally, we establish several identities that relate the rank weight distribution of a linear code to that of its dual code. One of our identities is the counterpart of the MacWilliams identity for the Hamming metric, and it has a different form from the identity by Delsarte.

Keywords

Cite

@article{arxiv.cs/0702077,
  title  = {Properties of Rank Metric Codes},
  author = {Maximilien Gadouleau and Zhiyuan Yan},
  journal= {arXiv preprint arXiv:cs/0702077},
  year   = {2007}
}

Comments

44 pages, 3 figures. Submitted to IEEE Transactions on Information Theory on March 6th