Characters, Weil sums and c-differential uniformity with an application to the perturbed Gold function

Building upon the observation that newly defined Ellingsen, et al. (2020) concept of c-differential uniformity is not invariant under EA or CCZ-equivalence Hasan (2021), we showed in Stanica and Geary (2021) adding some appropriate linearized monomials increases inverse function, significantly, for c. We continue investigation here. First, by analyzing involved equations, find bounds Gold function perturbed a single monomial, exhibiting discrepancy previously observed on function. Secondly, to treat general case perturbations via any polynomial, use characters finite field express all entries c-Differential Distribution Table (DDT) an (n, n)-function ${\mathbb {F}}_{p^{n}}$ , further, method explicit expressions c-DDT (via arbitrary polynomial).