Rank metric codes and their Galois duality

Abstract

In this paper, we describe the Galois dual of rank metric codes in the ambient space $F_Q^{n\times m}$ and $F_{Q^m}^n$, where Q=q^e. We obtain connections between the duality of rank metric codes with respect to distinct Galois inner products. Furthermore, for 0 ≤ s < e, we introduce the concept of q^sm-dual bases of F_Q^m over F_Q and obtain some conditions about the existence of q^sm-self-dual basis.