§3.2: Subspaces and decision trees

In this section we treat the domain of a boolean function as ${\mathbb F}_2^n$, an $n$-dimensional vector space over the field ${\mathbb F}_2$. As mentioned earlier, it can be natural to index the Fourier characters $\chi_S : {\mathbb F}_2^n \to \{-1,1\}$ not by subsets $S \subseteq [n]$ but by their $0$-$1$ indicator vectors $\gamma [...]