Constant-rank codes

Author

Gadouleau, Maximilien ; Yan, Zhiyuan

Author_Institution

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

fYear

2008

fDate

6-11 July 2008

Firstpage

876

Lastpage

880

Abstract

Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random network coding. In this paper, we show that constant- rank codes are closely related to constant-dimension codes and we study the properties of constant-rank codes. We first introduce a relation between vectors in GF(q^m)ⁿ and subspaces of GF(q)^m or GF(q)ⁿ, and use it to establish a relation between constant- rank codes and constant-dimension codes. We then derive bounds on the maximum cardinality of constant-rank codes with given rank weight and minimum rank distance. Finally, we investigate the asymptotic behavior of the maximal cardinality of constant- rank codes with given rank weight and minimum rank distance.

Keywords

channel coding; error correction codes; random codes; asymptotic behavior; constant-dimension codes; constant-rank codes; error control; minimum rank distance; noncoherent random network coding; rank weight; Electronic mail; Error correction; Galois fields; Network coding; Network topology; Public key cryptography; Transmitters; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory, 2008. ISIT 2008. IEEE International Symposium on

Conference_Location

Toronto, ON

Print_ISBN

978-1-4244-2256-2

Electronic_ISBN

978-1-4244-2257-9

Type

conf

DOI

10.1109/ISIT.2008.4595112

Filename

4595112