[n] \   | \   c_i  = 1 \},$$ where $[n] := \{1,2,...,n\}.$ So in the example above, $\text{supp(}c_1\text{)} = \{2,3\}$, $\text{supp(}c_2\text{)} = \{1,3\}$, $\text{supp(}c_3\text{)} = \{3\}$, and $\text{supp(}c_4\text{)} = \emptyset$. By dropping the set notation, we can write $C$ in shorthand as $C = \{\emptyset, 3, 13, 23\}$.

As mentioned in the previous section, neurons such as place cells fire in specific regions of a stimulus space known as receptive fields. For a (nonempty) stimulus space $X$, let $\mathcal{U} = \{U_1, U_2, ..., U_n\}$, where each $U_i \subseteq X$ is the receptive field of neuron $i$. Then we can define the associated receptive field code as $$C(\mathcal{U}) = \{  c \in \mathbb{F}_2^n \ | \ (\cap_{i \in \text{supp(}c\text{)}} U_i) \setminus (\cup_{j \notin \text{supp(}c\text{)}} U_j) \}.$$ In addition, for any point $p \in X$, we will let $c(p)$ denote the codeword such that $\text{supp(}c(p)\text{)} = \{i \in [n] \ | \ p \in U_i \}$. Going back to our example, the code $C = \{\emptyset, 3, 13, 23\}$ is the receptive field code for the set $\mathcal{U} = \{ U_1, U_2, U_3 \}$ shown in Figure \[fig:Ex1\].

(-2,-2) rectangle (4,2); (1,0) circle (1.7cm) node at (1,1) [$U_3$]{}; (.15,0) circle (.6cm) node 