Title

On the q-bentness of Boolean functions

Document Type

Article

Publication Title

Designs, Codes, and Cryptography

Publication Date

1-15-2019

Abstract

For each non-constant q in the set of n-variable Boolean functions, the q-transform of a Boolean function f is related to the Hamming distances from f to the functions obtainable from q by nonsingular linear change of basis. Klapper conjectured that no Boolean function exists with its q-transform coefficients equal to ±2n/2 (such function is called q-bent) when q is non-affine balanced. In our early work, we only gave partial results to confirm this conjecture for small n. Here we prove thoroughly that the conjecture is true for all n by investigating the nonexistence of the partial difference sets in abelian groups with special parameters. We also introduce a new family of functions called (δ, q) -bent functions, which give a measurement of q-bentness.

Volume

87

Issue

1

First Page

163

Last Page

171

DOI

10.1007/s10623-018-0494-1

ISSN

09251022

E-ISSN

15737586

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