Several secondary methods for constructing bent-negabent functions

In this paper, we present three secondary methods for constructing bent-negabent functions under the frameworks of the indirect sum construction (proposed by Carlet in 2004), the modified indirect sum construction (proposed by Hod.zi ' c et al in Des Codes Cryptogr 88(10):2007-2035, 2020) and Rothaus' construction. We first give a construction of bent-negabent functions by using the indirect sum construction, and specify some sufficient conditions on initial functions so that these constructed functions are provably outside the completed Maiorana-McFarland class. Here, we correct some results on the construction of bent-negabent functions proposed by Zhang et al. (IEEE Trans Inf Theory 61(3):1496-1506, 2015). Then, we investigate the nega-Hadamard transform of the composition of a multioutput function and a Boolean function. Using this tool, with initial primary bent-negabent functions, we analyze and find out the necessary and sufficient conditions for the modified indirect sum construction and Rothaus' construction to generate bent-negabent functions. Furthermore, by developing methods to obtain initial functions satisfying the required necessary and sufficient conditions, we propose several constructions of bent-negabent functions under these two frameworks of the secondary constructions.

Automated summary

In this paper, three secondary methods for constructing bent-negabent functions under different frameworks are presented. The necessary and sufficient conditions for generating these functions are analyzed. Several constructions are proposed based on these frameworks.