Generalized Semi-bent and Partially Bent Boolean Functions
نویسنده
چکیده
In this article, a relationship between the Walsh-Hadamard spectrum and σ f , the sum-of-squares-modulus indicator (SSMI) of the generalized Boolean function is presented. It is demonstrated for every s-plateaued generalized Boolean function in n variables that σ f = 22n+s. Two constructions on generalized semi-bent Boolean functions are presented. A class of generalized semi-bent functions in (n + 1) variables is constructed from generalized bent Boolean functions in n variables, and identify a subclass of it for which σ f = 22n+1 and △ f = 2 n+1 2 . Further, some constructions on generalized partially bent Boolean functions are presented at end of the article.
منابع مشابه
On generalized semi-bent (and partially bent) Boolean functions
In this paper, we obtain a characterization of generalized Boolean functions based on spectral analysis. We investigate a relationship between the Walsh-Hadamard spectrum and σ f , the sum-of-squares-modulus indicator (SSMI) of the generalized Boolean function. It is demonstrated that σ f = 22n+s for every s-plateaued generalized Boolean function in n variables. Two classes of generalized semi-...
متن کاملComplete Characterization of Generalized Bent and 2k-Bent Boolean Functions
In this paper we investigate properties of generalized bent Boolean functions and 2-bent (i.e., negabent, octabent, hexadecabent, et al.) Boolean functions in a uniform framework. We generalize the work of Stǎnicǎ et al., present necessary and sufficient conditions for generalized bent Boolean functions and 2-bent Boolean functions in terms of classical bent functions, and completely characteri...
متن کاملConstructions of Generalized Bent Boolean Functions on Odd Number of Variables
In this paper, we investigate the constructions of generalized bent Boolean functions defined on with values in Z4. We first present a construction of generalized bent Boolean functions defined on with values in Z4. The main technique is to utilize bent functions to derive generalized bent functions on odd number of variables. In addition, by using Boolean permutations, we provide a specific me...
متن کاملOn cross-correlation spectrum of generalized bent functions in generalized Maiorana-McFarland class
In this paper, we obtain the cross-correlation spectrum of generalized bent Boolean functions in a subclass of MaioranaMcFarland class (GMMF). An affine transformation which preserve the cross-correlation spectrum of two generalized Boolean functions, in absolute value is also presented. A construction of generalized bent Boolean functions in (n+ 2) variables from four generalized Boolean funct...
متن کاملSecondary constructions on generalized bent functions
In this paper, we construct generalized bent Boolean functions in n + 2 variables from 4 generalized Boolean functions in n variables. We also show that the direct sum of two generalized bent Boolean functions is generalized bent. Finally, we identify a set of affine functions in which every function is generalized bent.
متن کامل