Secondary constructions of bm$p$-ary (non-)weakly regular bent functions

Abstract

Bent functions can be used in many areas, such as symmetric cryptography, sequence design, and association schemes. In this paper, a generic secondary 构造 of bent functions from indirect sum and semi-direct sum methods is presented. Our method can be used to construct high algebraic degree (non-)weakly regular bent functions by employing suitable initial (vectorial) bent functions or their combinations. More precisely, we present some classes of (weakly) regular bent functions by using vectorial $\mathcal{M}$-$\mathcal{M}$ (Maiorana-McFarland) and $\mathcal{PS}$ (partial spread) bent functions, respectively. In particular, the explicit expressions for the dual of these (weakly) regular bent functions are obtained. Based on the vectorial perfect nonlinear ($\mathrm{PN}$) functions, infinite families of non-weakly regular bent functions can also be produced.