New infinite families of p-ary weakly regular bent functions

The characterization and construction of bent functions are challenging problems. The paper generalizes the constructions of Boolean bent functions by Mesnager [33], Xu et al. [40] and p-ary bent functions by Xu et al. [41] to the construction of p-ary weakly regular bent functions and presents new infinite families of p-ary weakly regular bent functions from some known weakly regular bent functions (square functions, Kasami functions, and the Maiorana-McFarland class of bent functions). Further, new infinite families of p-ary bent idempotents are obtained. Index Terms Bent functions, weakly regular bent functions, bent idempotents, Walsh transform, algebraic degree