On the generalization of the Costas property in higher dimensions

We investigate the generalization of the Costas property in threeor more dimensions, and we seek an appropriate definition; the two main complicationsare a) that the number of ''dots'' this multidimensional structureshould have is not obvious, and b) that the notion of the multidimensionalpermutation needs some clarification. After proposing various alternatives forthe generalization of the definition of the Costas property, based on the definitionsof the Costas property in one or two dimensions, we also offer someconstruction methods, the main one of which is based on the idea of reshapingCostas arrays into higher-dimensional entities.