Properties of Rank Metric Codes

Details Properties of Rank Metric Codes Properties of Rank Metric Codes

2007-02-13

arxiv.org/abs/cs/0702077v3

Computer Science

Information Theory

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

Scientific paper

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.

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