Using double Weil sums in finding the c-boomerang connectivity table for monomial functions on finite fields

In this paper we characterize the c-Boomerang Connectivity Table (BCT), c not equal 0 (thus, including the classical c = 1 case), for all monomial function xd in terms of characters and Weil sums on the finite field F-pn, for an odd prime p. We further simplify these expressions for the Gold functions xp(k)+ 1 for all 1 <= k < n, and p odd. It is the first such attempt for a complete description for the classical BCT and its relative c-BCT, for all parameters involved, albeit in terms of characters.