F_q^n-linear rank distance codes and their distinguishers
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For any admissible value of the parameters there exist Maximum Rank distance (shortly MRD) F_q^n-linear codes of F_q^n× n. It has been shown in H-TNRR (see also ByrneRavagnani) that, if field extensions large enough are considered, then almost all (rectangular) rank distance codes are MRD. On the other hand, very few families of 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 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 Gabidulin, see also Loi06,PWZ,WT. In this work, we will survey the known families of 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 GiuZ.
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