Generalized Permutations and Ternary Bent Functions

TL;DR

This paper explores generating ternary bent functions through spectral permutations and introduces generalized permutations that produce new bent functions, including a class capable of generating all 2-place ternary bent functions from a small set of seed functions.

Contribution

It introduces spectral invariant operations for ternary bent functions and identifies a permutation class with a Kronecker product structure for comprehensive generation.

Findings

Spectral permutations can generate new bent functions.

A class of permutations with Kronecker structure is identified.

All 2-place ternary bent functions can be generated from 9 seed functions.

Abstract

The report studies the generation of ternary bent functions by permuting the circular Vilenkin_Chrestenson spectrum of a known bent function. We call this spectral invariant operations in the spectral domain, in analogy to the spectral invariant operations in the domain of the functions. Furthermore, related generalized permutations are derived to obtain new bent functions in the original domain. In the case of 2_place ternary bent functions a class of permutations with a Kronecker product structure is disclosed, which allows generating all 2_place ternary bent functions, based on a set of 9 seed functions.