Decomposing generalized bent and hyperbent functions
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Authors
Martinsen, Thor
Meidl, Wilfried
Mesnager, Sihem
Stănică, Pantelimon
Subjects
Boolean functions
Walsh-Hadamard transforms
Bent functions
semi-bent functions
Hyper bent functions
Generalized bent functions
Cyclotomic fields
Walsh-Hadamard transforms
Bent functions
semi-bent functions
Hyper bent functions
Generalized bent functions
Cyclotomic fields
Advisors
Date of Issue
2016-04-12
Date
Publisher
Language
Abstract
In this paper we introduce generalized hyperbent functions from F2n to Z2k, and investigate decompositions of generalized (hyper)bent functions. We show that generalized (hyper)bent functions from F2n to Z2k consist of components which are generalized
(hyper)bent functions from F2n to Z2k′ for some k′ < k. For odd n, we show that the Boolean functions associated to a generalized bent function form an affine space of semibent functions.
This complements a recent result for even n, where the associated Boolean functions are bent.
Type
Article
Description
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Second author is supported by the Austrian Science Fund (FWF)
Funder
Project number. M 1767-N26
Format
24 p.
Citation
arXiv:1604.02830 [cs.IT]
Distribution Statement
Rights
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.