2024 On the duals of generalized bent functions

On the duals of generalized bent functions

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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 … 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 …

08. Introduction to generalized functions (distributions)

Webbent 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 ... Web5 de nov. de 2024 · Recall that G k precisely contains the duals of the bent functions in F k (and vice versa). Note that for two divisors k 2 > k 1 of m with gcd( p m − 1 , p k i + p − 1) = 1, downloading pictures from motorola g7

Constructing new superclasses of bent functions from known …

Web1 de set. de 1985 · GENERALIZED BENT FUNCTIONS 99 Many of the constructions for bent functions over Jg provided in Section VI result in bent functions whose Fourier … 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 … 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 … class 8 science chapter 11 answers

Generic Constructions of (Boolean and Vectorial) Bent Functions …

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

WebThis enables us to completely characterize generalized bent functions and $\mathbb Z_{p^{k}}$ -bent functions by some affine space associated with the generalized bent … 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‐ class 8 science chapter 11 notes byjusWeb4 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 … class 8 science ch-9

"WebQuadratic bent functions and their duals. 14 June 2024. Kanat Abdukhalikov, Rongquan Feng & Duy Ho. A survey on p-ary and generalized bent functions. 01 April 2024. ... Feng, K. Q., Generalized bent functions and class number of imaginary quadratic fields, Science in China, Ser. A, 2001, 44(5): 562–570. " - On the duals of generalized bent functions

On the duals of generalized bent functions

WebScience China Mathematics - Several new results on non-existence of generalized bent functions are presented. The results are related to the class number of imaginary … 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 ...

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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 … 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 ...

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 … Web1 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 …

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 … 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 …

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 …

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). downloading pictures from phone windows 10Web4 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 … class 8 science chapter 11 explanationWebThree 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 ... downloading pictures from samsung phone to pcWebWe 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 … class 8 science chapter 11 testWeb14 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 … class 8 science chapter 10 book pdfWebDuals 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 … downloading pictures from the cloud to pcWebAbstract: 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 … downloading pictures from my phone