Question: How to define a set with certain properties?

How can I define a set generated by two degree n polynomials with binary coefficients?

For example: for n=2, I want to generate the set {(a_0*x_0+a_1*x_1)* (b_0*y_0+b_1*y_1) s.t. a_0,a_1,b_0,b_1 are binary}. 

Thank you in advance.

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