2 research outputs found
Properties of Rank Metric Codes
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.Comment: 44 pages, 3 figures. Submitted to IEEE Transactions on Information
Theory on March 6t
Error performance analysis of maximum rank distance codes
In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes that parallel those of maximum distance separable (MDS) codes. Using these properties, we show that, for MRD codes with error correction capability t, the decoder error probability of bounded distance decoders decreases exponentially with t2 based on the assumption that all errors with the same rank are equally likely. Finally, our simulation results show that our bounds seem applicable to other error models as well and that MRD codes are more resilient against crisscross errors than MDS codes. I