Each row of a Hadamard matrix is perpendicular to the previous one.
And hadamard gates implement conditional qbit operations.
Even in 1940 thinking, multiplying u by r meant figuring what the ciphertect would have been should the rotor have rotated the u.
What we want after n rebounds of des is that if u consider each round output to be ur then ur and ur2 differ as do rows on the hadamard matrix.
Ie half the bit differ.
Which is more tangible than “avalanche” since now we had a limiting condition – when the sequence of conditionals has induced the cipher text itself to be/become an action matrix ;that only produces outputs indistinguishable from uniformity)
In q terms, the data under a long sequence of qbit manipulation has itself evolved to become a hadamard action…
Ok so that means we have a replicating group. We have an expander whose action is to output a (key/plaintext parameyerizrd) expander code that is itself an action…