Generation of Ternary Bent Functions by Spectral Invariant Operations in the Generalized Reed-Muller Domain

Abstract

Spectral invariant operations for ternary functions are defined as operations that preserve the absolute values of Vilenkin-Chrestenson spectral coefficients. Ternary bent functions are characterized as functions with a flat Vilenkin-Chrestenson spectrum, i.e., functions all whose spectral coefficients have the same absolute value. It follows that any function obtained by the application of one or more spectral invariant operations to a bent function will also be a bent function. This property is used in the present study to generate ternary bent functions efficiently in terms of space and time. For a software implementation of spectral invariant operations it is convenient to specify functions to be processed by the generalized Reed- Muller expressions. In this case, each invariant operation over a function f corresponds to adding one or more terms to the generalized Reed-Muller expression for f.