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I want to gerate a random function from $GF(2)^4$ to $GF(2)^4$. So my function takes 4 bit input value and 4 bit output value. Also how to define if my function is say $f(x_1,x_2,x_3,x_4)=(x_1 \oplus x_2, x_3, x_4,x_1)$?

I want to gerate generate a random function from $GF(2)^4$ to $GF(2)^4$. So my function takes 4 bit input value and 4 bit output value. Also how to define if my function is say $f(x_1,x_2,x_3,x_4)=(x_1 \oplus x_2, x_3, x_4,x_1)$?