Gibbs Characterization of a Class of Quaternary Bent Functions

As already noticed in previous chapters, there are differences between binary bent functions and bent functions for \(p>2\) . For example, the binary bent functions are defined as maximally non-linear binary functions. In the case of bent functions for other values of p, including the case \(p=4\) this feature does not necessarily hold. As pointed out in [1] for quaternary functions, and discussed more generally for any p in [2], there are quaternary bent functions that are not maximally non-linear, and, vice versa, maximally non-linear quaternary functions that are not bent.