Remarks on Similarities among Ternary Bent Functions

Abstract

Bent functions have low autocorrelation and it is interesting to consider if there are some relationships that may be found among values a bent function takes, i.e., to find some possible patterns expressing similarity among certain bent functions in terms of the structure of their value-vectors. A possible approach towards exploring that problem proposed in this paper is based on partial Vilenkin-Chrestenson spectra, which are conveniently interpreted as matrix-valued Vilenkin-Chrestenson spectra of matrix-valued equivalents of ternary bent functions.