On the duals of generalized bent functions

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 … 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 an odd prime, is a positive integer. It is known that weakly regular generalized bent functions always appear in pairs since the dual of a weakly regular generalized bent function is …

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Web29 de jul. de 2011 · We classify all self dual and anti self dual quadratic bent functions in 2 n variables under the action of the orthogonal group { {O} (2n,\mathbb F_2)} . This is … 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. birdhouse signs https://bakerbuildingllc.com

On the Dual of Generalized Bent Functions

WebBoolean bent functions introduced by Rothaus [35] play an important role in cryptography, coding theory, sequences and combinatorics. In 1985, Kumar et al. [16] generalized Boolean bent functions to bent functions over finite fields of odd characteristic. Due to the importance of bent functions, they have been studied extensively. There is an ... WebDuals 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. 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). damaged lymphatic system ankles

Further constructions of bent functions and their duals

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On the duals of generalized bent functions

Duals of non-weakly regular bent functions are not weakly …

Web7 de jun. de 2024 · Abstract. In this paper, we study the dual of generalized bent functions f: V n → Z p k where V n is an n -dimensional vector space over F p and p is an odd … WebWe 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 …

On the duals of generalized bent functions

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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 ... WebRecently, Li et al. presented a generic construction of bent functions in [IEEE Trans. Inf. Theory, vol. 68, no. 4, pp. 2735-2751, 2024]. In this paper, we give a characterization for their ...

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 … 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 ...

Web1 de nov. de 2024 · We demonstrate that many known constructions can be derived from our proposed construction as special cases by choosing proper initial functions and parameters. By modifying the new construction, a novel secondary construction of generalized bent functions from two initial generalized bent functions is obtained. Web1 de out. de 2013 · We analyse a recently introduced construction of non-weakly regular bent functions and show conditions under which their dual is bent as well. This leads to …

Web4 de jan. de 2024 · [16,17]. Bent functions always occur in pairs and their duals are also bent. Bent functions have two subclasses; self dual bent functions and anti-self dual bent functions, see [3]. Some new constructions of bent functions are recently introduced by Mes-nager [12]. We here present some new constructions of bent functions. Any …

Web14 de jun. de 2015 · For a special class of generalized Boolean bent functions with even number of variables constructed from a class of quadratic binary bent functions in … damaged luggage claim chase sapphireWeb1 de jun. de 2024 · The class of dual-bent functions containing the class of weakly regular bent functions as a proper subclass is defined, and self-duality for bent functions in … birdhouse sites osrsWebThree 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 ... bird house sites osrsWeb15 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 … damaged lyrics post maloneWebbent 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 ... damaged luggage claim american airlinesWeb{"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 ... damaged lyrics tlcWebBesides 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‐ bird houses in trees images