  We leverage proof techniques Fourier analysis and an existing result in
coding theory to derive new bounds for the problem of non-interactive
simulation of binary random variables. Previous bounds in the literature were
derived by applying data processing inequalities concerning maximal correlation
or hypercontractivity. We show that our bounds are sharp in some regimes. For a
specific instance of problem parameters, our main result answers an open
problem posed by E. Mossel in 2017. As by-products of our analyses, various new
properties of the average distance and distance enumerator of binary block
codes are established.
