see lol i'm reading the perturbed error correcting code paper and just https://people.csail.mit.edu/akavia/AV_PerturbationCodes.pdf

The perturbation operator, given a generating matrix R ∈ k×n {0, 1} of any binary linear code R, outputs a generating matrix P ert(R) of a new binary linear code P ert(R). The columns of the generating matrix P ert(R) are sums (modulo 2) r ⊕ of columns r of R and vectors from k low dimensional subspaces of {0, 1} .

it's RIDICULOUS to describe a stateful serial data flow (the earlier bits are literally being sent first!) with a matrix transform like the perturbations are completely independent.

maybe if your message is going to be stored in the persistent storage device on a satellite orbiting the sun this matrix assumption could make sense. but if you can't design a basic automaton (doesn't have to be a whole turing machine!!) for a stateful transformation and you're name dropping fucking adi shamir???? then yes i absolutely do think less of you and for work for that!

We think of the sums r ⊕ as a perturbation of the column r by. Specifically, the columns of P ert(R) are all sums r ⊕ for r ∈ Ri , ∈ Li, i = 1, . . . , Θ(n) for Ri and Li chosen as follows.

oh jesus FUCKING christ they're not even like.......using that matrix to simulate perturbation on the message at all. the matrix is apparently a representation for an expander graph of some kind??

and a uniformly random r ∈ Ri,

or maybe not at all, maybe they're just a statistician and they don't a god damn clue what they're doing