A couple of things occur to me, thinking back to 1954.
First, one should think of a rotor as a means of producing distance (or difference). One thinks of the input set as a relative frequency. The inner product of the two is a particular space, where one deals with mean-set – based on random walks. A sequence of rotors produces the weight function when the “domain of definition” covers every vertice, with its atomic probability measure. With this condition, we enter a world of :total definition, which allows the notion of minimum distance to be the same as minim weight, which is a measure of the mean set in the asymptotic limit.
Second, the polish breakthrough in early enigma cryptanalysis was based on cataloging the conjugacy classes for particular substitutions of boxed alphabet (to use GCCS terms). The very notion of public key becomes apparent, back in 1954 terms, when the secret value s, as in w is conjugated by s giving t, operates in a world where t is only one member of the conjugacy class. This if course was the case with enigma/cyclometer cryptanlaysis