balanced function (thing)
Return to balanced function (thing)
This can be extended to functions over other finite fields (GF(qn) → GF(pm), with qn ≥ pm): a function is said to be balanced if it is surjective and every element of the codomain occurs with equal probability, across all possible inputs.
As an example, let's look at the output of a boolean function (GF(23) → GF(2)):
x0 = 0, x1 = 0, x2 = 0 → f(x0,x1,x2) = 0
As we can see, over all 8 possible combinations of inputs you get zero 4 times as output and you get one 4 times as well, which indicates that this boolean function (called "majority function") is balanced.