Email me at jantrobus@
My office is in Patterson Office Tower 722.
My mailbox is in POT 715.
Office in POT 722
Mailbox in POT 715
This semester, I can be found Monday 10am to 11am in the Mathskeller. I am available to meet at other times throughout the week by appointment.
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.
Let $R$ be a finite principal left ideal ring. Via a total ordering of the ring elements and an ordered basis a lexicographic ordering of the module $R^n$ is produced. This is used to set up a greedy algorithm that selects vectors for which all linear combinations with the previously selected vectors satisfy a pre-specified selection property and updates the to-be-constructed code to the linear hull of the vectors selected so far. The output is called a lexicode. This process was discussed earlier in the literature for fields and chain rings. In this paper we investigate the properties of such lexicodes over finite principal left ideal rings and show that the total ordering of the ring elements has to respect containment of ideals in order for the algorithm to produce meaningful results. Only then it is guaranteed that the algorithm is exhaustive and thus produces codes that are maximal with respect to inclusion. It is further illustrated that the output of the algorithm heavily depends on the total ordering and chosen basis.
Chris Christensen and Jared Antrobus describe the clever mathematics used to decipher a World War II Japanese code.