On $q$-nearly bent Boolean functions
Abstract
For each non-constant Boolean function , Klapper introduced the notion of -transforms of Boolean functions. The {\em -transform} of a Boolean function is related to the Hamming distances from to the functions obtainable from by nonsingular linear change of basis. In this work we discuss the existence of -nearly bent functions, a new family of Boolean functions characterized by the -transform. Let be a non-affine Boolean function. We prove that any balanced Boolean functions (linear or non-linear) are -nearly bent if has weight one, which gives a positive answer to an open question (whether there exist non-affine -nearly bent functions) proposed by Klapper. We also prove a necessary condition for checking when a function isn't -nearly bent.
Keywords
Cite
@article{arxiv.1905.00150,
title = {On $q$-nearly bent Boolean functions},
author = {Zhixiong Chen and Andrew Klapper},
journal= {arXiv preprint arXiv:1905.00150},
year = {2019}
}