منابع مشابه
On the representation of bent functions by bent rectangles
We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to construct bent functions, improve a lower bound for the number of bent functions. 1 Preliminaries Let Vn be an n-dimensional vector space over the field F2 = {0, 1} ...
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It is proved that no non-quadratic Kasami bent is affine equivalent to MaioranaMacFarland type bent functions.
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A bent function is a Boolean function all of whose Fourier coefficients are equal in absolute value. These functions have been extensively studied in cryptography and play an important role in cryptanalysis and design of cryptographic systems. We study bent functions in the framework of property testing. In particular, we show that testing whether a given Boolean function on n variables is bent...
متن کاملOn the degree of homogeneous bent functions
It is well known that the degree of a 2m-variable bent function is at most m. However, the case in homogeneous bent functions is not clear. In this paper, it is proved that there is no homogeneous bent functions of degree m in 2m variables when m > 3; there is no homogenous bent function of degree m− 1 in 2m variables when m > 4; Generally, for any nonnegative integer k, there exists a positive...
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In 1990 Kechris and Louveau developed the theory of three very natural ranks on the Baire class 1 functions. A rank is a function assigning countable ordinals to certain objects, typically measuring their complexity. We extend this theory to the case of Baire class ξ functions, and generalize most of the results from the Baire class 1 case. We also show that their assumption of the compactness ...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2007
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2007.03.001