I think the most canonical example of historical uses of codes are the enigma machines used by the German military forces in World War II and their decryption by the codebreakers at Bletchley Park.
Those codes are relatively easy to understand as building upon the letter transposition as per the Caesar cypher, which allows simple examples to be followed in the classroom. It is very easy to get the students to write sample codes that allow them to see how the encryption works starting with the daily setup of the enigma machine. With modern computers at their disposal, even replicating the extra rotor of the German Navy enigma machines isn’t very problematic.
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