A Singleton Bound for Generalized Ferrers Diagram Rank Metric Codes

In this paper, we will employ the technique used in the proof of classical Singleton bound to derive upper bounds for rank metric codes and Ferrers diagram rank metric codes. These upper bounds yield the rank distance Singleton bound and an upper bound presented by Etzion and Silberstein respectively. Also we introduce generalized Ferrers diagram rank metric code which is a Ferrers diagram rank metric code where the underlying rank metric code is not necessarily linear. A new Singleton bound for generalized Ferrers diagram rank metric code is obtained using our technique.

[1]  Ron M. Roth,et al.  Author's Reply to Comments on 'Maximum-rank array codes and their application to crisscross error correction' , 1991, IEEE Trans. Inf. Theory.

[2]  Richard C. Singleton,et al.  Maximum distance q -nary codes , 1964, IEEE Trans. Inf. Theory.

[3]  Frank R. Kschischang,et al.  Coding for Errors and Erasures in Random Network Coding , 2007, IEEE Transactions on Information Theory.

[4]  E. Knill,et al.  Theory of quantum error-correcting codes , 1997 .

[5]  Natalia Silberstein,et al.  Error-Correcting Codes in Projective Spaces Via Rank-Metric Codes and Ferrers Diagrams , 2008, IEEE Transactions on Information Theory.

[6]  Alexander Vardy,et al.  Error-Correcting Codes in Projective Space , 2011, IEEE Trans. Inf. Theory.

[7]  Viola,et al.  Theory of quantum error correction for general noise , 2000, Physical review letters.

[8]  Richard M. Wilson,et al.  A course in combinatorics , 1992 .

[9]  Raymond Laflamme,et al.  A Theory of Quantum Error-Correcting Codes , 1996 .

[10]  B. Sundar Rajan,et al.  A lattice singleton bound , 2013, 2013 IEEE International Symposium on Information Theory.