Functions with high nonlinearity have important applications in cryptography, sequences and coding theory. The purpose of this paper is to give a well-rounded treatment of non-Boolean functions with optimal nonlinearity. We summarize and generalize known results, and prove a number of new results. We also present open problems about functions with high nonlinearity. © 2003 Elsevier Inc. All rights reserved.
Carlet, C., & Ding, C. (2004). Highly nonlinear mappings. Journal of Complexity, 20(2–3), 205–244. https://doi.org/10.1016/j.jco.2003.08.008