  For any admissible value of the parameters there exist Maximum Rank distance
(shortly MRD) $\mathbb{F}_{q^n}$-linear codes of $\mathbb{F}_q^{n\times n}$. It
has been shown in \cite{H-TNRR} (see also \cite{ByrneRavagnani}) that, if field
extensions large enough are considered, then \emph{almost all} (rectangular)
rank distance codes are MRD. On the other hand, very few families of
$\mathbb{F}_{q^n}$-linear codes are currently known up to equivalence. One of
the possible applications of MRD-codes is for McEliece--like public key
cryptosystems, as proposed by Gabidulin, Paramonov and Tretjakov in \cite{GPT}.
In this framework it is very important to obtain new families of MRD-codes
endowed with fast decoding algorithms. Several decoding algorithms exist for
Gabidulin codes as shown in \cite{Gabidulin}, see also \cite{Loi06,PWZ,WT}. In
this work, we will survey the known families of $\mathbb{F}_{q^n}$-linear
MRD-codes, study some invariants of MRD-codes and evaluate their value for the
known families, providing a characterization of generalized twisted Gabidulin
codes as done in \cite{GiuZ}.
