Note on Budaghyan and Carlet's almost perfect nonlinear functions

Almost perfect nonlinear (APN) functions have good prop-erties and are widely applied in sequence design and coding theory. Budaghyan and Carlet (2008) [5] constructed a family of APN hexanomials F3 over F22m with a certain technical condition. In this article, we give the number of APN hex-anomials F3 and support a determination theorem for APN hexanomials F3 if i = 1. Moreover, we construct a family of APN functions in bivariate form and show it is CCZ-equivalent to F3. (c) 2023 Elsevier Inc. All rights reserved.