Im starting to see how 1950s crypto wheel wiring theory – based on permutation group theory – has all the same elements as we know in (nkd) code making. That is, we want the equivalent of a dual space matrix that encodes invariants that induce generators of a cayley graph whose resulting sequences enumerate each of the elementary group operation for any group elements.
The linkage between the world of wheel wirings that are generating each codeword and the world of stochastic transformations comes when the seeing the k generators differently, seeing them now as the k cycles that may make up a particular generator value.
If the goal is to exploit the contraction properties of the perron-frobenius invariant based on the time evolution being attracted to a fixed point attractor (associated with a unique stationary distiribution of the infinitesimal stochastic operator), the powers of k generators (that must sum to zero) can now be seen as rotations of or indexes into the k co-cycles of the given generator.
This directly equates now with denoting the space of hamming parity matrix as that formed when all the constraints encoded within the matrix and collectively acting on a purported codeword vector map to zero