Odd cross-intersection bound ($|\mathcal{A}||\mathcal{B}|\le 2^{n+1}$)

Appending a coordinate one to each indicator vector changes every odd cross-intersection dot product into an even one in ${\mathbb{F}}_2^{n+1}$. The argument for the even cross-intersection bound then gives the displayed bound. It is a valid bound without a claim that it is sharp.