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A bent function from F 2 n to F 2 , n even, can be transformed into a negabent function, or slightly more general into a bent 4 , also called shifted bent function, by adding a certain quadratic term. If n is odd, then negabent functions similarly correspond to semibent functions with some additional property. Whereas bent functions induce relative difference sets in F 2 n × F 2 , negabent functions induce relative difference sets in F 2 n − 1 × Z 4 . We analyse equivalence of negabent functions respectively of their relative difference sets. We show that equivalent bent functions can correspond to inequivalent negabent functions, hence one can obtain inequivalent relative difference sets in F 2 n − 1 × Z 4 with EA-equivalence. We also show that this is not the case when n is odd. Finally we analyse the class of semibent functions that corresponds to negabent functions and show that though partially bent semibent functions always can be shifted to negabent or bent 4 functions, there are many semibent functions which do not correspond to negabent and bent 4 functions. [ABSTRACT FROM AUTHOR]

For c ∈ F 2 n , a c -bent 4 function f from the finite field F 2 n to F 2 is a function with a flat spectrum with respect to the unitary transform V f c , which is designed to describe the component functions of modified planar functions. For c = 0 the transform V f c reduces to the conventional Walsh transform, and hence a 0-bent 4 function is bent. In this article we generalize the concept of partially bent functions to the transforms V f c . We show that every quadratic function is partially bent, and hence it is plateaued with respect to any of the transforms V f c . In detail we analyse two quadratic monomials. The first has values as small as possible in its spectra with respect to all transforms V f c , and the second has a flat spectrum for a large number of c . Moreover, we show that every quadratic function is c -bent 4 for at least three distinct c . In the last part we analyse a cubic monomial. We show that it is c -bent 4 only for c = 1 , the function is then called negabent, which shows that non-quadratic functions exhibit a different behaviour. [ABSTRACT FROM AUTHOR]