Browsing by Author "Meidl, Wilfried"
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Bent and vectorial bent functions, partial difference sets, and strongly regular graphs
Çesmelioğlu, Ayça; Meidl, Wilfried (Amer Inst Mathematical SciencesAims, 2018)Bent and vectorial bent functions have applications in cryptography and coding and are closely related to objects in combinatorics and finite geometry, like difference sets, relative difference sets, designs and divisible ... 
Bent functions, spreads, and opolynomials
Çeşmelioğlu, Ayça; Meidl, Wilfried; Pott, Alexander (Siam Publications, 2015)We show that bent functions f from F(p)m x F(p)m to Fp, which are constant or affine on the elements of a given spread of F(p)m x F(p)m, either arise from partial spread bent functions, or they are Boolean and a generalization ... 
Non weakly regular bent polynomials from vectorial quadratic functions
Çeşmelioğlu, Ayça; Meidl, Wilfried (Amer Mathematical Soc, 2015)The Fourier spectrum of some classes of vectorial quadratic functions is analysed. We obtain counting functions for vectorial quadratic functions with prescribed Fourier spectrum using discrete Fourier transform. Vectorial ... 
Partially bent functions and their properties
Çeşmelioğlu, Ayça; Meidl, Wilfried; Topuzoğlu, Alev (Cambridge Univ Press, 2014)A function f : Fp(n) > Fp is called partially bent if for all a is an element of Fp(n) the derivative D(a)f(x) = f(x + a)  f(x) is constant or balanced, i.e., every value in Fp is taken on p(n1) times. Bent functions ... 
There are infinitely many bent functions for which the dual is not bent
Ceşmelioğlu, Ayça; Meidl, Wilfried; Pott, Alexander (IeeeInst Electrical Electronics Engineers Inc, 2016)Bent functions can be classified into regular bent functions, weakly regular but not regular bent functions, and nonweakly regular bent functions. Regular and weakly regular bent functions always appear in pairs, since ... 
Vectorial bent functions and their duals
Çesmelioğlu, Ayça; Meidl, Wilfried; Pott, Alexander (Elsevier Science Inc, 2018)Motivated 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 the study of duality for ...