On Properties of the Rounded Zhang-Hartley Transform

Abstract

A new transform is introduced by rounding the values of entries in the Zhang-Hartley Transform matrix to integers making in this way the transform better adapted to integer-valued functions that will be processed. The new transform is integer-valued, but however, it inherits from the complex-valued Vilenkin-Chrestenson transform, the capability of characterizing ternary bent functions with a flat circular spectrum, albeit for a smaller class of bent functions. The characterization is obtained independently of the basic value set {0, 1, 2} or {−1, 0, 1} that are both usually used in ternary valued functions. This follows from the property that change of the basic value set can be viewed as encoding of function values, which is an operation preserving bentness.