“We study the fundamental challenge of exhibiting explicit functions that have small correlation with low-degree polynomials over 𝔽₂. Our main contributions include: …
2) We propose a new approach for proving correlation bounds with the central ‘mod functions.’ …
3) We prove our conjecture for quadratic polynomials. … We express correlation in terms of directional derivatives and analyze it by slowly restricting the direction.
4) We make partial progress on the conjecture for cubic polynomials, in particular proving tight correlation bounds for cubic polynomials whose degree-3 part is symmetric.”

Find the paper and full list of authors at the Dagstuhl Research Online Publication Server.