they often provide strictly higher security than the known security provided by other MRD codes [@allertonversion Sec. IV-B].

Organization of the paper
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After some preliminaries in Section II, the paper is organized as follows: In Section III, we give lower and upper bounds on the GRWs of reducible codes, extending the lower bound on the minimum rank distance given in [@reducible], and see that the given upper bound on the minimum rank distance can be reached by some reduction. In Section IV, we obtain new parameters for which reducible codes are MRD (or close to MRD) and with MRD components, and obtain explicit estimates on their GRWs, including those MRD codes found in [@reducible] and considered for secure network coding in [@silva-universal]. In Section V, we obtain all linear codes whose GRWs are all optimal, for all fixed packet and code sizes, up to rank equivalence. In Section VI, we see that the actual information leakage occuring when using reducible codes is often much less than the worst case given by their GRWs, providing higher security than other known MRD codes. Finally, in Section VII, we study secondary but related properties: Conditions to be rank equivalent to cartesian products 