On the duals of generalized bent functions

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‐ WebQuadratic AB (almost bent) functions are characterized by the property that the du-als of their component functions are bent functions. We prove that these duals are also quadratic and illustrate that these bent duals may give rise to vectorial bent functions (in certain cases having a maximal output dimension). It is then natural to ...

New Secondary Constructions of Generalized Bent Functions

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 … 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 ... imed healthcare portal https://procus-ltd.com

Constructing new superclasses of bent functions from known …

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 ... 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 … 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). imed gregory hills

New Secondary Constructions of Generalized Bent Functions

Category:Enumeration of the bent functions of least deviation from a …

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On the duals of generalized bent functions

Constructing new superclasses of bent functions from known …

Web1 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 … Web1 de jan. de 2024 · Meidl W A secondary construction of bent functions, octal gbent functions and their duals Math. Comput. Simul. 2024 143 57 64 3698215 10.1016/j.matcom.2016.02.003 Google Scholar Digital Library; 10. Meidl W Pott A Generalized bent functions into Z p k from the partial spread and the Maiorana …

On the duals of generalized bent functions

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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 … Web6 de jun. de 2024 · 06/06/21 - 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 ...

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. 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 …

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, 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 …

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, ...

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. imed helpWebIt 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 regular generalized … imed helplineWeb1 de jun. de 2024 · Duals of non-weakly regular bent functions are not weakly regular and generalization to plateaued functions. Author links open overlay panel Ferruh Özbudak … imed herstonWebQuadratic 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. … list of neurosesWebTo 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 … imed hetrinWeb2 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 … imed heaths roadWebBoolean 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 ... imed hematology