Further Results on Bent–Negabent Boolean Functions

Characterization and Properties of Bent‐Negabent Functions

“…The necessary and sufficient condition that defined in Corollary 1 is bent‐negabent has been proposed in Ref. [18].…”

“…which was introduced by Ref. [17]. In the following, based on the generalized composition theorem, the nega-Hadamard transform of this generalized indirect sum can be obtained easily.…”

“…The secondary construction is an efficient way to generate more Boolean (or bent) functions [1,16,17] . An important secondary construction of bent functions is the classical Carlet's construction (or called the indirect sum) [16] which defined as…”

Investigations on <i>c</i>-Bent₄ Functions via the Unitary Transform and <i>c</i>-Correlation Functions

“…In the following, based on the methods of the construction of bent-negabent functions discussed in [8], the unitary transform of the classical Carlet's construction and a necessary and sufficient condition for function ℎ defined as in ( 12) to be 𝑐-bent 4 can be obtained easily.…”

“…Inspired by this work, we concentrate on the unitary transform in more detail, and our first contribution is to present several results on the behavior of the unitary transform on various combinations of Boolean functions. In [15], the classical Carlet's construction (or called the indirect sum) of Boolean functions is presented, and in [8] a class of bent-negabent functions is given by using the indirect sum construction. Then our second contribution is to provide the unitary transform of the indirect sum construction and give a necessary and sufficient condition so that the indirect sum construction to be 𝑐-bent 4 functions.…”