GENp1-1: Properties of Codes with the Rank Metric

Author

Gadouleau, Maximilien ; Yan, Zhiyuan

Author_Institution

Dept. of Electr. & Comput. Eng., Lehigh Univ., Bethlehem, PA

fYear

2006

fDate

Nov. 27 2006-Dec. 1 2006

Firstpage

1

Lastpage

5

Abstract

In this paper, we study properties of rank metric codes in general and maximum rank distance (MRD) codes in particular. For codes with the rank metric, we first establish Gilbert and sphere-packing bounds, and then obtain the asymptotic forms of these two bounds and the Singleton bound. Based on the asymptotic bounds, we observe that asymptotically Gilbert-Varsharmov bound is exceeded by MRD codes and sphere-packing bound cannot be attained. We also establish bounds on the rank covering radius of maximal codes, and show that all MRD codes are maximal codes and all the MRD codes known so far achieve the maximum rank covering radius.

Keywords

codes; public key cryptography; Gilbert-Varsharmov bound; Singleton bound; asymptotic bound; maximum rank distance codes; public-key cryptosystems; rank metric codes; sphere-packing bound; Block codes; Communication channels; Decoding; Error correction codes; Hamming weight; Public key; Public key cryptography; Security; Wireless communication;

fLanguage

English

Publisher

ieee

Conference_Titel

Global Telecommunications Conference, 2006. GLOBECOM '06. IEEE

Conference_Location

San Francisco, CA

ISSN

1930-529X

Print_ISBN

1-4244-0356-1

Electronic_ISBN

1930-529X

Type

conf

DOI

10.1109/GLOCOM.2006.173

Filename

4150803