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This paper investigates the construction of rank-metric codes with specified Ferrers diagram shapes. These codes play a role in the multilevel construction for subspace codes. A conjecture from 2009 provides an upper bound for the dimension of a rank-metric code with given specified Ferrers diagram shape and rank distance. While the conjecture in its generality is wide open, several cases have been established in the literature. This paper contributes further cases of Ferrers diagrams and ranks for which the conjecture holds true. In addition, the proportion of maximal Ferrers diagram codes within the space of all rank-metric codes with the same shape and dimension is investigated. Special attention is being paid to MRD codes. It is shown that for growing field size the limiting proportion depends highly on the Ferrers diagram. For instance, for $[m\times 2]$ -MRD codes with rank 2 this limiting proportion is close to $1/e$. [ABSTRACT FROM AUTHOR]

By the end of 1943, US Navy mathematician/codebreaker Marshall Hall Jr. had developed a system of statistical weights to align JN-25 messages in depth. Although then-current methods of aligning JN-25 messages in depth were working satisfactorily, Hall developed his method "just in case." On 1 December 1943, the Japanese changed the method of numbering the lines and columns of additives on pages of the JN-25 additive book, and Hall's weights, which had been developed "just in case," were needed immediately. This paper discusses both the mathematical idea that was the foundation of Hall's weights and the construction of the weights. It also explores the navy's use of the weights as well as their use at Bletchley Park. At the same time, the navy was exploring the use of two other systems of weights to align JN-25 messages in depth, and those systems of weights are also described. [ABSTRACT FROM AUTHOR]

A postwar report shows that during World War II, OP-20-GM, the research section of Naval Communications, planned and the Naval Computing Machine Laboratory engineered and produced at least 27 different codebreaking machines or attachments, and did developmental work on others. This is the story of one of those machines: Mamba. The documentation relating to Mamba is thorough enough that it is possible to track the development of Mamba from an idea based upon the garble-check properties built into the Japanese naval ciphers JN-25 and JN-11 through planning and engineering to a finished machine. [ABSTRACT FROM PUBLISHER]