Two skew cyclic codes can be equivalent for the Hamming metric only if they
have the same length, and only the zero code is degenerate. The situation is
completely different for the rank metric, where lengths of codes correspond to
the number of outgoing links from the source when applying the code on a
network. We study rank equivalences between skew cyclic codes of different
lengths and, with the aim of finding the skew cyclic code of smallest length
that is rank equivalent to a given one, we define different types of length for
a given skew cyclic code, relate them and compute them in most cases. We give
different characterizations of rank degenerate skew cyclic codes using
conventional polynomials and linearized polynomials. Some known results on the
rank weight hierarchy of cyclic codes for some lengths are obtained as
particular cases and extended to all lengths and to all skew cyclic codes.
Finally, we prove that the smallest length of a linear code that is rank
equivalent to a given skew cyclic code can be attained by a pseudo-skew cyclic
code. Throughout the paper, we find new relations between linear skew cyclic
codes and their Galois closures
