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arXiv · 2208.02378

Multidimensional Costas Arrays and Their Periodicity

Ivelisse Rubio·Jaziel Torres
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Abstract

A novel higher-dimensional definition for Costas arrays is introduced. This definition works for arbitrary dimensions and avoids some limitations of previous definitions. Some non-existence results are presented for multidimensional Costas arrays preserving the Costas condition when the array is extended periodically throughout the whole space. In particular, it is shown that three-dimensional arrays with this property must have the least possible order; extending an analogous two-dimensional result by H. Taylor. Said result is conjectured to extend for Costas arrays of arbitrary dimensions.

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Ivelisse Rubio, Jaziel Torres. 2022-08-03. Multidimensional Costas Arrays and Their Periodicity. https://arxiv.org/abs/2208.02378

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