Some results on q-ary bent functions

Kumar et al.(1985) have extended the notion of classical bent Boolean functions in the generalized setup on Zq . They have provided an analogue of classical Maiorana-McFarland type bent functions. In this paper, we study the crosscorrelation of a subclass of such generalized MaioranaMcFarland (GMMF) type bent functions. We provide a construction of quaternary (q = 4) bent functions on n + 1 variables in terms of their subfunctions on n-variables. Analogues of sum-ofsquares indicator and absolute indicator of crosscorrelation of Boolean functions are defined in the generalized setup. Further, q-ary functions are studied in terms of these indictors and some upper bounds of these indicators are obtained. Finally, we provide some constructions of balanced quaternary functions with high nonlinearity under Lee metric.