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 b...

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Bibliographic Details
Published in:Chinese Journal of Electronics 2022-07, Vol.31 (4), p.786-792
Main Authors: JIANG, Niu, ZHAO, Min, YANG, Zhiyao, ZHUO, Zepeng, CHEN, Guolong
Format: Article
Language:English
Subjects:
Bent‐negabent function
Boolean function
Nega‐Hadamard transform
Walsh‐Hadamard transform
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Summary: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.
ISSN:1022-4653
2075-5597
DOI:10.1049/cje.2021.00.417