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.
['Maximilien Gadouleau', 'Zhiyuan Yan']
Constant-rank codes