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Skew cyclic codes play the same role as cyclic codes in the theory oferror-correcting codes for the rank metric. In this paper, we give descriptionsof these codes by root spaces, cyclotomic spaces and idempotent generators. Weprove that the lattice of skew cyclic codes is anti-isomorphic to the latticeof root spaces, study these two lattices and extend the rank-BCH bound on theirminimum rank distance to rank-metric versions of the van Lint-Wilson's shiftand Hartmann-Tzeng bounds. Finally, we study skew cyclic codes which are linearover the base field, proving that these codes include all Hamming-metric cycliccodes, giving then a new relation between these codes and rank-metric skewcyclic codes.

On the roots and minimum rank distance of skew cyclic codes