On the duals of generalized bent functions

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August undefined, 2024

Webpointed in [28]. The complete characterization of generalized bent functions from diﬀerent perspectives was recently presented in [13,35,25]. A comprehensivesurvey on existing generalizations of bent functions can be found in [36]. For every bent Boolean function its dual bent functions is uniquely deﬁned. It is important to note that the ... Web25 de mar. de 2024 · Abstract: In this paper, we study the duals of generalized bent functions Z , where is an -dimensional vector space over F and is an odd prime, is a positive integer. It is known that weakly regular generalized bent functions always …

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Web9 de fev. de 2024 · Weakly normal bent functions, Bent duals, 4-bent decomposition 1. Introduction An important class of Boolean functions was introduced by Rothaus [20] in 1976, which are de ned in even number of variables having the maximum possible Hamming distance to the set of all a ne functions. Web6 de jun. de 2024 · This leads to the definition of the class of dual-bent functions containing the class of weakly regular bent functions as a proper subclass. We analyse self … birds of paradise inuyasha

Constructing new superclasses of bent functions from known …

Web4 de jan. de 2024 · This article is devoted to Boolean and vectorial bent functions and their duals. Our ultimate objective is to increase such functions’ corpus by designing new ones covering many previous bent functions’ constructions. To this end, we provide several new infinite families of bent functions, including idempotent bent functions of any algebraic … Web26 de ago. de 2012 · We study a construction of the bent functions of least deviation from a quadratic bent function, ... New nonexistence results on (m, n)-generalized bent functions. 02 January 2024. Ka Hin Leung & Qi Wang. ... Quadratic bent functions and their duals. 14 June 2024. Kanat Abdukhalikov, ... Web22 de mar. de 2024 · In Sect. 4, we consider the design of bent functions by selecting 5-valued spectra functions in the generalized Maiorana-McFarland class. ... Several new infinite families of bent functions and their duals. IEEE Trans. Inf. Theory 60(7), 4397–4407 (2014). birds of paradise katong

Generic Constructions of (Boolean and Vectorial) Bent Functions …

Bent and vectorial bent functions, partial difference sets, and ...

Web2 I. INTRODUCTION Throughout this paper, let p be an odd prime, Zpk be the ring of integers modulo pk, Fn p be the vector space of the n-tuples over Fp, Fpn be the ﬁnite ﬁeld with pn elements and Vn be an n-dimensional vector space over Fp where k,n are positive integers. Boolean bent functions introduced by Rothaus [14] play an important … Web2 I. INTRODUCTION Throughout this paper, let pbe an odd prime, Z pk be the ring of integers modulo pk, Fn be the vector space of the n-tuples over F p, F pn be the ﬁnite ﬁeld with pn elements and V n be an n-dimensional vector space over F p where k;nare positive integers. Boolean bent functions introduced by Rothaus [14] play an important role in … danbury ct birth certificateWebDuals of non-weakly regular bent functions are not weakly regular and generalization to plateaued functions. Author links open overlay panel Ferruh Özbudak a, Rumi Melih … birds of paradise lyrics kaskade

"WebThree new secondary constructions of generalized bent functions are presented. We provide a secondary construction of generalized bent functions from indirect sum methods proposed by Carlet et al. A ... " - On the duals of generalized bent functions

On the duals of generalized bent functions

$arXiv:2107.13538v1 [math.CO] 28 Jul 2024$

Web6 de jun. de 2024 · On the Dual of Generalized Bent Functions. 06/06/2024. by Jiaxin Wang, et al. 0. share. In this paper, we study the dual of generalized bent functions … Web4 de jan. de 2024 · This article is devoted to Boolean and vectorial bent functions and their duals. Our ultimate objective is to increase such functions’ corpus by designing new …

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WebExtensions/Duals 3. Topological details: families of seminorms 4. Examples of continuous linear functionals (distributions) 5. Colimit topology on D(Rn) 6. Distributions supported at 0 7. Weak dual topologies (weak -topologies) 8. Di erentiation of generalized functions (distributions) 9. Multiplication of generalized functions by smooth ... Web15 de mar. de 2024 · By generalizing the construction of Çeşmelioğlu et al. , 2016, we provide an explicit construction of generalized bent functions whose duals can be …

Web1 de jan. de 2024 · We observe that every octal gbent function in even dimension is essentially equivalent to a bent function obtained with Carlets secondary construction of bent functions from three bent functions with certain properties. We use this strong connection to ... Web{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,7]],"date-time":"2024-04-07T04:44:00Z","timestamp ...

WebBesides that, the explicit duals of all bent functions constructed by this work are also ob-tained, which not only enables us to give explicitly the duals of bent functions in Corollary 2 of [11], but also makes it possible for us to construct some self‐dual bent functions. Moreover, we are also able prove that our bent functions can be EA‐ Web6 de jun. de 2024 · On the Dual of Generalized Bent Functions. In this paper, we study the dual of generalized bent functions where is an -dimensional vector space over and is …

WebAbstract: We exhibit a simple condition under which the sum (modulo 2) of characteristic functions of (n/2)-dimensional vector subspaces of (GF(2))/sup n/ (n even) is a Bent function. The "Fourier" transform of such a Bent function is the sum of the characteristic functions of the duals of these spaces. The class of Bent functions that we obtain …

WebTo design new bent functions is an eternal theme for researchers. There are direct and indirect ways for construction of bent functions. The former is also called primary … danbury ct board of educationhttp://www.m-hikari.com/ija/ija-2024/ija-1-4-2024/p/sharmaIJA1-4-2024.pdf danbury ct bathroom vanitiesWebDuals of non-weakly regular bent functions are not weakly regular and generalization to plateaued functions. Author links open overlay panel Ferruh Özbudak a, Rumi Melih Pelen b. ... In 2013, Çesmelioğlu, Meidl and Pott pointed out that the existence of a non-weakly regular bent function having weakly regular bent dual is an open problem. birds of paradise kharadiWeb1 de mai. de 1976 · Let P(x) be a function from GF(2 n) to GF(2). P(x) is called “bent” if all Fourier coefficients of (−1) P(x) are ±1. The polynomial degree of a bent function P(x) is … birds of paradise lionsgate apple tvWeb1 de jul. de 2024 · It is known that weakly regular generalized bent functions always appear in pairs since the dual of a weakly regular generalized bent function is also a weakly … danbury ct building department permitsWebWe introduce and study dual functions of generalized Boolean bent functions over ℤ 4, i.e., functions from F 2-vector spaces to ℤ 4 whose Fourier transforms have constant … danbury ct birth certificate copyWebbent function, [4, 12]. Obviously bent functions only exist if nis even, and then W f(u) = 2n=2( 1)f (x) for a Boolean function f(x), called the dual of f. As is well known, the dual f is also a bent function. For an integer qlet Z q be the ring of integers modulo q. For a generalized Boolean function ffrom V n to Z 2k, k 1, the generalized ... danbury ct bathroom installation