Title :
Constant-rank codes
Author :
Gadouleau, Maximilien ; Yan, Zhiyuan
Author_Institution :
Dept. of Electr. & Comput. Eng., Lehigh Univ., Bethlehem, PA
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(qm)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;
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
DOI :
10.1109/ISIT.2008.4595112
