Construction methods for generalized bent functions
نویسندگان
چکیده
منابع مشابه
Construction methods for generalized bent functions
Generalized bent (gbent) functions is a class of functions f : Z 2 → Zq, where q ≥ 2 is a positive integer, that generalizes a concept of classical bent functions through their codomain extension. A lot of research has recently been devoted towards derivation of the necessary and sufficient conditions when f is represented as a collection of Boolean functions. Nevertheless, apart from the neces...
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In this paper, we investigate the properties of generalized bent functions defined on Z2 with values in Zq , where q ≥ 2 is any positive integer. We characterize the class of generalized bent functions symmetric with respect to two variables, provide analogues of Maiorana–McFarland type bent functions and Dillon’s functions in the generalized set up. A class of bent functions called generalized...
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The notions of perfect nonlinearity and bent functions are closely dependent on the action of the group of translations over IF2 . Extending the idea to more generalized groups of involutions without fixed points gives a larger framework to the previous notions. In this paper we largely develop this concept to define G-perfect nonlinearity and G-bent functions, where G is an Abelian group of in...
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A (I, -1 )-matrix will be called a bent type matrix if each row and each column are bent sequences. A similar description can be found in Carlisle M. Adams and Stafford E. Tavares, Generating and counting binary sequences, IEEE Trans. Inform. Theory, vol. 36, no. 5, pp. 1170-1173, 1990, in which the authors use the properties of bent type matrices to construct a class of bent functions. In this...
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In this paper we characterize (octal) bent generalized Boolean functions defined on Z2 with values in Z8. Moreover, we propose several constructions of such generalized bent functions for both n even and n odd.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2018
ISSN: 0166-218X
DOI: 10.1016/j.dam.2017.11.027