Hi everybody,

I would much appreciate if anyone could assist me with the following problem:

Given:

consider a 4-bit input vector

, with .

Now consider a function

, with and ,

i.e. the component functions are Boolean functions of algebraic degree .

Now consider two functions that have the following properties:

with the component functions

also being Boolean functions but only with an algebraic degree .

denote the two 4-bit output vectors of and .

Wanted:

I am looking for Boolean functions with algebraic degree , such that

holds.

I have already looked at Matlab, but it seems that it does not supports Boolean algebra

Does anyone has any idea how to approach this problem?

Thanks!