On Semibent Boolean Functions

We show that any Boolean function, in even dimension, equal to the sum of a Boolean function g which is constant on each element of a spread and of a Boolean function h whose restrictions to these elements are all linear, is semibent if and only if g and h are both bent. We deduce a large number of...

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Bibliographic Details
Published in:IEEE transactions on information theory 2012-05, Vol.58 (5), p.3287-3292
Main Authors: Carlet, C., Mesnager, S.
Format: Article
Language:English
Subjects:
Applied sciences
Bent function
Boolean function
Boolean functions
Computer science
Constrictions
Correlation
Cryptography
Exact sciences and technology
Information theory
Information, signal and communications theory
Mathematical functions
partial spread class
Polynomials
semibent function
Spreads
Telecommunications and information theory
three-valued almost optimal function
Transforms
Vectors
Walsh Hadamard transform
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Summary:We show that any Boolean function, in even dimension, equal to the sum of a Boolean function g which is constant on each element of a spread and of a Boolean function h whose restrictions to these elements are all linear, is semibent if and only if g and h are both bent. We deduce a large number of infinite classes of semibent functions in explicit bivariate (respectively, univariate) polynomial form.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2181330