Towards the Gibbs Characterization of a Class of Quaternary Bent Functions

Abstract

Bent functions generalized to the alphabet Zq, the ring of integers modulo q, are interesting not just in the realm of multiple-valued functions, but have some applications in the binary environment. The case q = 4, i.e., quaternary bent functions, are of a particular interest due to a simple relationship to binary functions. We consider the possibilities for characterization of quaternary bent functions in terms of the Gibbs derivatives defined with respect to the Reed-Muller-Fourier (RMF) transform for q-valued functions. It is shown that quaternary bent functions can be split into classes of functions sharing the same values for their Gibbs derivatives.