The title actually claims it all – I am not pretty absolutely sure if this is solvable. I have two vectors A and C and I want to make a vector B so that the marriage amongst the mutual information and facts I(A,B C) is purely synergistic (ie XOR(A, B) = C). The capture is that A and C are not binary vectors: they array from -3 for A and -4 for C. EDIT – I am in fact not certain if this is feasible if A and C are now correlated as A is will often release data about C no matter of the construction of the other variable.

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As long as the valid state space is equally large for all 3, you can create a 1:1 mapping function. You may want a commutative function (like XOR, after applying the mapping).

Do you have any other requirements? Why do you need this?

Also see format preserving encryption, which is relevant when you need to maintain the size and format of the original messages.

B is A xor C