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For any admissible value of the parameters there exist Maximum Rank distance(shortly MRD) $\mathbb{F}_{q^n}$-linear codes of $\mathbb{F}_q^{n\times n}$. Ithas been shown in \cite{H-TNRR} (see also \cite{ByrneRavagnani}) that, if fieldextensions 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 ofthe possible applications of MRD-codes is for McEliece--like public keycryptosystems, as proposed by Gabidulin, Paramonov and Tretjakov in \cite{GPT}.In this framework it is very important to obtain new families of MRD-codesendowed with fast decoding algorithms. Several decoding algorithms exist forGabidulin codes as shown in \cite{Gabidulin}, see also \cite{Loi06,PWZ,WT}. Inthis work, we will survey the known families of $\mathbb{F}_{q^n}$-linearMRD-codes, study some invariants of MRD-codes and evaluate their value for theknown families, providing a characterization of generalized twisted Gabidulincodes as done in \cite{GiuZ}.

$\mathbb{F}_{q^n}$-linear rank distance codes and their distinguishers