Landscape Boolean functions

Constanza Riera; Pantelimon Stănică

doi:10.3934/amc.2019038

Article Contents

2019, Volume 13, Issue 4: 613-627. Doi: 10.3934/amc.2019038

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Landscape Boolean functions

Constanza Riera^1, and
Pantelimon Stănică^2, ,

1.
Department of Computing, Mathematics, and Physics, Western Norway University of Applied Sciences, 5020 Bergen, Norway
2.
Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA

^* Corresponding author: Pantelimon Stănică
^* Corresponding author: Pantelimon Stănică

Received: October 2018

Published: June 2019

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Abstract

In this paper we define a class of generalized Boolean functions defined on $ {\mathbb F}_2^n $ with values in $ {\mathbb Z}_q $ (we consider $ q = 2^k $, $ k\geq 1 $, here), which we call landscape functions (whose class contains generalized bent, semibent, and plateaued) and find their complete characterization in terms of their Boolean components. In particular, we show that the previously published characterizations of generalized plateaued Boolean functions (which includes generalized bent and semibent) are in fact particular cases of this more general setting. Furthermore, we provide an inductive construction of landscape functions, having any number of nonzero Walsh-Hadamard coefficients. We also completely characterize generalized plateaued functions in terms of the second derivatives and fourth moments.

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Mathematics Subject Classification: Primary: 94C10; Secondary: 06E30, 11A07.

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References

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