Chapter 16 - Combinatorial Generalizations of Bent Functions

Abstract

In this chapter we consider generalizations or subclasses based on some combinatorial ideas. We consider bent functions with some special properties—for example, with items of algebraic normal form being of the same degree (homogeneous functions), or highly symmetric bent functions (symmetric and rotation-symmetric bent functions) or bent functions that are constant/affine on subspaces (normal/weakly normal functions). We also consider non-Boolean functions similar to bent functions. In the sphere of our interest, there are symmetric bent functions, homogeneous bent functions, rotation-symmetric bent functions, normal bent functions, self-dual and anti-self-dual bent functions, partially defined bent functions, plateaued functions, Z-bent functions and negabent functions.