Characterization and Properties of Bent-Negabent Functions

A further characterization of the bent-negabent functions is presented. Based on the concept of complete mapping polynomial, we provide a necessary and sufficient condition for a class of quadratic Boolean functions to be bent-negabent. A new characterization of negabent functions can be described by using the parity of Hamming weight. We further generalize the classical convolution theorem and give the nega-Hadamard transform of the composition of a Boolean function and a vectorial Boolean function. The nega-Hadamard transform of a generalized indirect sum is calculated by this composition method.

Automated summary

This paper presents a further characterization of bent-negabent functions, providing a necessary and sufficient condition for a class of quadratic Boolean functions to be bent-negabent based on complete mapping polynomial concept. A new characterization of negabent functions is described using the parity of Hamming weight. The paper also extends the classical convolution theorem and calculates the nega-Hadamard transform of the composition of a Boolean function and a vectorial Boolean function.