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In this paper, a Roos like bound on the minimum distance for skew cycliccodes over a general field is provided. The result holds in the Hamming metricand in the rank metric. The proofs involve arithmetic properties of skewpolynomials and an analysis of the rank of parity-check matrices. For the rankmetric case, a way to arithmetically construct codes with a prescribed minimumrank distance, using the skew Roos bound, is also given. Moreover, someexamples of MDS codes and MRD codes over finite fields are built, using theskew Roos bound.

Roos bound for skew cyclic codes in Hamming and rank metric