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This article is cited in 1 scientific paper (total in 1 paper)
Discrete Functions
On some properties of self-dual generalized bent functions
A. V. Kutsenkoab a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Abstract:
Bent functions of the form $\mathbb{F}_2^n\rightarrow\mathbb{Z}_q$, where $q\geqslant2$ is a positive integer, are known as generalized bent (gbent) functions. A gbent function for which it is possible to define a dual gbent function is called regular. A regular gbent function is said to be self-dual if it coincides with its dual. We obtain the necessary and sufficient conditions for the self-duality of gbent functions from Eliseev — Maiorana — McFarland class. We find the complete Lee distance spectrum between all self-dual functions in this class and obtain that the minimal Lee distance between them is equal to $q\cdot2^{n-3}$. For Boolean case, there are no affine bent functions and self-dual bent functions, while it is known that for generalized case affine bent functions exist, in particular, when $q$ is divisible by $4$. We prove the non-existence of affine self-dual gbent functions for any natural even $q$. A new class of isometries preserving self-duality of a gbent function is presented. Based on this, a refined classification of self-dual gbent functions of the form $\mathbb{F}_2^4\rightarrow\mathbb{Z}_4$ is given.
Keywords:
self-dual bent function, generalized bent function, Eliseev — Maiorana — McFarland bent function, Lee distance.
Citation:
A. V. Kutsenko, “On some properties of self-dual generalized bent functions”, Prikl. Diskr. Mat. Suppl., 2021, no. 14, 42–45
Linking options:
https://www.mathnet.ru/eng/pdma526 https://www.mathnet.ru/eng/pdma/y2021/i14/p42
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Abstract page: | 110 | Full-text PDF : | 54 | References: | 18 |
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