Title :
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
fDate :
Nov. 27 2006-Dec. 1 2006
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;
Conference_Titel :
Global Telecommunications Conference, 2006. GLOBECOM '06. IEEE
Conference_Location :
San Francisco, CA
Print_ISBN :
1-4244-0356-1
Electronic_ISBN :
1930-529X
DOI :
10.1109/GLOCOM.2006.173
