On the roots and minimum rank distance of skew cyclic codes

Skew cyclic codes play the same role as cyclic codes in the theory of errorcorrecting codes for the rank metric. In this paper, we give descriptions of these codes by idempotent generators, root spaces and cyclotomic spaces. We prove that the lattice of skew cyclic codes is anti-isomorphic to the lattice of root spaces and extend the rank-BCH bound on their minimum rank distance to rank-metric versions of the van Lint-Wilson’s shift and Hartmann-Tzeng bounds. Finally, we study skew cyclic codes which are linear over the base field, proving that these codes include all classical cyclic codes equipped with the Hamming metric.