In Bogdanov's and others, PRESENT: An Ultra-Lightweight Block Cipher, they mention that the S-box in PRESENT fulfill four primary conditions. They denote the Fourier coefficient as $$S_b^W (a) = \sum_{x\in \mathbb{F}_2^4} (-1) ^{\langle b, S(x)\rangle+\langle a,x \rangle}.$$
I am trying to understand what conditions (3) and (4) are trying to say. They are:
(3) For all non-zero $a\in \mathbb{F}_2^4$ and all non-zero $b\in \mathbb{F}_2^4$ it holds that $|S_b^W|\leq 8$.
(4) For all $a \in \mathbb{F}_2^4$ and all non-zero $b \in \mathbb{F}_2^4$ such that $wt(a) = wt(b) = 1$ it holds that $S_b^W (a) = \pm 4$
How does one raise a power to Bogdanov's notation (or compute such sum)?