On the generalization of the Costas property to higher dimensions

Details On the generalization of the Costas property to higher dimensions On the generalization of the Costas property to higher dimensions

2007-01-21

arxiv.org/abs/math/0701582v1

Mathematics

Combinatorics

Scientific paper

We investigate the generalization of the Costas property in 3 or more dimensions, and we seek an appropriate definition; the 2 main complications are a) that the number of ``dots'' this multidimensional structure should have is not obvious, and b) that the notion of the multidimensional permutation needs some clarification. After proposing various alternatives for the generalization of the definition of the Costas property, based on the definitions of the Costas property in 1 or 2 dimensions, we also offer some construction methods, the main one of which is based on the idea of reshaping Costas arrays into higher-dimensional entities.

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