On the Nonexistence of q -Bent Boolean Functions

We continue the study of the properties of Boolean functions as reflected in The properties of a recently defined transform. For each non-constant Boolean function q , the q - transform of a Boolean function f is related to the Hamming distances from f to the functions obtainable from q by n...

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Bibliographic Details
Published in:IEEE transactions on information theory 2018-04, Vol.64 (4), p.2953-2961
Main Authors: Klapper, Andrew, Chen, Zhixiong
Format: Article
Language:English
Subjects:
Bent function
Boolean algebra
Boolean function
Boolean functions
Ciphers
Codes
Correlation
Hamming distance
Properties (attributes)
Transforms
Walsh-Hadamard transform
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Summary:We continue the study of the properties of Boolean functions as reflected in The properties of a recently defined transform. For each non-constant Boolean function q , the q - transform of a Boolean function f is related to the Hamming distances from f to the functions obtainable from q by nonsingular linear change of basis. Many properties that can be characterized by the Walsh-Hadamard transform have (for each q ) analogues that can be characterized by the q -transform. In this paper, we study one such property, bentness. We show that if q is balanced and not affine, then there is no function that is both bent and q -bent.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2017.2758788