Spectral invariance operations for the construction of ternary bent functions

Abstract

Ternary bent functions are characterized by a flat Vilenkin-Chrestenson (VC) spectrum, i.e., functions all whose spectral coefficients have the same absolute value. Spectral invariance operations for ternary functions are defined as operations that preserve the absolute values of VC spectral coefficients. It follows that any function obtained by the application of one or more spectral invariance operations to a bent function is also a bent function. This property is used in this study to generate ternary bent functions efficiently in terms of space and time, since we do not need to check if the functions produced by spectral invariance operations are bent. The proposed procedure is performed in the generalized Reed-Muller (RM) domain by referring to the degree of bent functions.