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Titlebook: Bent Functions and Permutation Methods; Binary and Multiple- Radomir S. Stanković,Milena Stanković,Jaakko Astol Book 2024 The Editor(s) (if

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期刊全称Bent Functions and Permutation Methods
期刊简称Binary and Multiple-
影响因子2023Radomir S. Stanković,Milena Stanković,Jaakko Astol
视频video
发行地址Discusses in a uniform way, the theory of binary, ternary, and quaternary bent functions.Describes differences between the types of functions, including spectral invariant operations and construction
学科分类Synthesis Lectures on Engineering, Science, and Technology
图书封面Titlebook: Bent Functions and Permutation Methods; Binary and Multiple- Radomir S. Stanković,Milena Stanković,Jaakko Astol Book 2024 The Editor(s) (if
影响因子.This book discusses in a uniform way binary, ternary, and quaternary bent functions, while most of the existing books on bent functions refer to just binary bent functions. The authors describe the differences between binary and multiple-valued cases and the construction methods for bent functions are focused on the application of two types of permutation matrices. These matrices are derived from a class of differential operators on finite groups and Fast Fourier transform algorithms, respectively. The approach presented is based on the observation that given certain bent functions, many other bent functions can be constructed by manipulating them. Permutations are possible manipulations that are easy to implement. These permutations perform spectral invariant operations which ensure that they preserve bentness..
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Construction of Bent Functions by FFT-like Permutation Matrices,ved in computing the corresponding spectral coefficients. The function values used to compute a spectral coefficient are uniquely determined by the positions from which the data are fetched in steps of FFT algorithms for the Walsh and the Vilenkin-Chrestenson transforms, respectively, for binary- and multiple-valued functions.
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Gibbs Characterization of a Class of Quaternary Bent Functions,oes not necessarily hold. As pointed out in [.] for quaternary functions, and discussed more generally for any . in [.], there are quaternary bent functions that are not maximally non-linear, and, vice versa, maximally non-linear quaternary functions that are not bent.
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Gibbs Characterization of Ternary Bent Functions,ry bent functions, a straightforward extension is impossible, and not all ternary bent functions can be conveniently characterized in terms of the Gibbs derivatives; still some interesting conclusions can be derived.
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