A note on generalized bent criteria for Boolean functions
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Authors
Gangopadhyay, Sugata
Pasalic, Enes
Stănică, Pantelimon
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Date of Issue
2012
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en_US
Abstract
In this paper, we consider the spectra of
Boolean functions with respect to the action of unitary transforms obtained by taking tensor products of the Hadamard kernel, denoted by H, and the nega–Hadamard kernel, denoted by N. The set of all such transforms is denoted by {H,N}n. A Boolean function
is said to be bent4 if its spectrum with respect to at least one unitary transform in {H,N}n is flat. We obtain a relationship between bent, semi–bent and bent4 functions,
which is a generalization of the relationship between bent and negabent Boolean functions proved by Parker and
Pott [cf. LNCS 4893 (2007), 9–23]. As a corollary to this result we prove that the maximum possible algebraic degree of a bent4 function on n variables is [n/2], and
hence solve an open problem posed by Riera and Parker [cf. IEEE-TIT 52:9 (2006), 4142–4159].
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.1109/TIT.2012.2235908.
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Applied Mathematics
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Naval Postgraduate School (U.S.)
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Citation
IEEE Transactions on Information Theory, Vol. XXX, No. Y, Month year
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.