NDLI: A Note on Generalized Bent Criteria for Boolean Functions

Content Provider	IEEE Xplore Digital Library
Author	Gangopadhyay, S. Pasalic, E. Stanica, P.
Copyright Year	1963
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, semibent, 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].
Sponsorship	IEEE Information Theory Society
Starting Page	3233
Ending Page	3236
Page Count	4
File Size	1121651
File Format	PDF
ISSN	00189448
Volume Number	59
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Boolean functions Transforms Zinc Next generation networking Cryptography Vectors Walsh–Hadamard transform Algebraic degree bent function ${\rm bent}_{4}$ function nega-Hadamard transform
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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A note on generalized bent criteria for boolean functions.

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