In [2,3], the so-called vectorial dual-bent functions are considered to construct partial difference sets. In [2], emelioluet al.showed that for certain vectorial dual-bent functionsF:Vn鈫扸s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts...
Recently, several interesting constructions of vectorial Boolean functions with the maximum number of bent components (MNBC functions, for short) were proposed. However, many of them have component functions from the completed Maiorana-McFarland class. Moreover, no examples of MNBC functions containin...
A SiOx layer and hydrophilic groups (e.g. -OH) have been thus formed on pre-bent PDMS substrates by the O2 plasma. When the strain of PDMS exceeds a critical value, the PDMS substrate self-assembles to form folded grating structures after bent relaxation18. By controlling the side on ...
& Bent, S. F. A brief review of atomic layer deposition: from fundamentals to applications. Mater. Today 17, 236–246 (2014). Article Google Scholar Aoni, R. A. et al. High-efficiency visible light manipulation using dielectric metasurfaces. Sci. Rep. 9, 6510 (2019). Article ADS ...
Vectorial bent functions and their dualsVectorial bent functionsDual of a bent functionMotivated by the observation that for two (weakly regular) bent functions f, g for which also f + g is bent, the sum f* + g* of their duals f and g* is sometimes but not always bent, we initiate...
Dual of a bent functionMotivated by the observation that for two (weakly regular) bent functions f,g f , g mathContainer Loading Mathjax for which also f+g f + g mathContainer Loading Mathjax is bent, the sum f +g f + g mathContainer Loading Mathjax of their duals f f math...
Let,be finite abelian groups. A functionffromAtoBis called abent functionif (1.1) for every characterofwhich is non-trivial onB. Equivalently,fis bent if and only if for all nonzerothe derivativein directiona, is balanced, i.e, every value ofBis taken on the same number, |A|/|B|,...
Recently, the first two authors showed that the elements which a vectorial dual-bent function with certain additional properties maps to 0, form a partial difference set, which generalizes the connection between Boolean bent functions and Hadamard difference sets, and some later established connections...
Vectorial bent functionsBent functions in odd characteristic can be either (weakly) regular or non-weakly regular. Furthermore one can distinguish between dual-bent functions, which are bent functions for which the dual is bent as well, and non-dual bent functions. Whereas a weakly regular bent...