On new Properties of the Maiorana-McFarland Ternary Bent Functions

Abstract

Maiorana-McFarland ternary bent functions are analyzed with respect to their relationship with spectral invariant operations and with respect to self-duality. In analogy to the Maiorana-McFarland method to generate binary bent functions, an equation is introduced to generate ternary bent functions in an even number of variables. It is shown that Maiorana-McFarland ternary bent functions are strict bent and that their duals may not be Maiorana-McFarland. It is known that spectral invariant operations preserve the bentness of a function. We show that most spectral invariant operations preserve that Maiorana-McFarland bentness of ternary functions. The concept of generalized self-duality is introduced and it is shown how Maiorana-McFarland ternary bent functions exhibit this kind of self-duality. It is shown that Maiorana-McFarland ternary bent functions in two variables may be divided into 3 classes of 54 functions each. A list of these functions for a first class is given in an Appendix.