Vectorial bent functions and their duals

Motivated by the observation that for two (weakly regular) bent functions f,g for which also f+g is bent, the sum f⁎+g⁎ of their duals f⁎ and g⁎ is sometimes but not always bent, we initiate the study of duality for vectorial bent functions. We propose and investigate two concepts of self-duality for vectorial bent functions, self-duality and weak self-duality.