  Reducible codes for the rank metric were introduced for cryptographic
purposes. They have fast encoding and decoding algorithms, include maximum rank
distance (MRD) codes and can correct many rank errors beyond half of their
minimum rank distance, which makes them suitable for error-correction in
network coding. In this paper, we study their security behaviour against
information leakage on networks when applied as coset coding schemes, giving
the following main results: 1) we give lower and upper bounds on their
generalized rank weights (GRWs), which measure worst-case information leakage
to the wire-tapper, 2) we find new parameters for which these codes are MRD
(meaning that their first GRW is optimal), and use the previous bounds to
estimate their higher GRWs, 3) we show that all linear (over the extension
field) codes whose GRWs are all optimal for fixed packet and code sizes but
varying length are reducible codes up to rank equivalence, and 4) we show that
the information leaked to a wire-tapper when using reducible codes is often
much less than the worst case given by their (optimal in some cases) GRWs. We
conclude with some secondary related properties: Conditions to be rank
equivalent to cartesian products of linear codes, conditions to be rank
degenerate, duality properties and MRD ranks.
