Functions with high nonlinearity have been an instrumental tool not only in algebra and finite geometries but also in combinatorics, coding theory and cryptography as well. Near perfect nonlinear (NPN) functions were introduced recently by Wen et al. [5], which can be viewed as an extension of perfect nonlinear (PN) function. In this paper, we present two constructions of NPN function and obtain new classes of NPN functions.

NPN function, sequence, difference-balanced property, trace function.