A secondary construction of bent functions, octal gbent functions and their duals

We observe that every octal gbent function in even dimension is essentially equivalent to a bent function obtained with Carlet's secondary construction of bent functions from three bent functions with certain properties. We use this strong connection to completely describe octal gbent functions in even dimension and their duals. This is also the first comprehensive treatment of duality for gbent functions. Implementations of this construction of bent functions also enable us to construct infinite classes of octal gbent functions and their duals. We present some examples.