Before revision:  Our negative results combine the Fourier analytic methods of Kapralov-Khanna-Sudan SODA'15 , which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results .
After revision:  Our negative results combine the Fourier analytic methods of Kapralov-Khanna-Sudan SODA'15 1\ .