Decomposition of bent generalized Boolean functions

TL;DR

This paper establishes a correspondence between generalized bent functions and tuples of Boolean bent functions, providing a new framework for classifying these functions under extended affine transformations.

Contribution

It introduces a one-to-one correspondence between regular generalized bent functions and tuples of Boolean bent functions, enhancing understanding and classification.

Findings

Established a correspondence between generalized and Boolean bent functions.

Mapped self-dual and anti-self-dual properties between functions.

Provided a classification method under the extended affine group.

Abstract

A one to one correspondence between regular generalized bent functions from $\F_2^n$ to $\Z_{2^m},$ and $m-$tuples of Boolean bent functions is established. This correspondence maps self-dual (resp. anti-self-dual) generalized bent functions to $m-$tuples of self-dual (resp. anti self-dual) Boolean bent functions. An application to the classification of regular generalized bent functions under the extended affine group is given.