1 research outputs found
On -nearly bent Boolean functions
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