On the dual of (non)-weakly regular bent functions and self-dual bent functions

For weakly regular bent functions in odd characteristic the dual function is also bent.We analyse a recently introduced construction of non-weakly regular bent functions andshow conditions under which their dual is bent as well. This leads to the definition ofthe class of dual-bent functions containing the class of weakly regular bent functions as a proper subclass.We analyse self-duality for bent functions in odd characteristic, and characterize quadraticself-dual bent functions. We construct non-weakly regular bent functions with and without abent dual, and bent functions with a dual bent function of a different algebraic degree.