Multidimensional Costas Arrays and Their Periodicity
Information Theory
2022-08-05 v1 math.IT
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.
Keywords
Cite
@article{arxiv.2208.02378,
title = {Multidimensional Costas Arrays and Their Periodicity},
author = {Ivelisse Rubio and Jaziel Torres},
journal= {arXiv preprint arXiv:2208.02378},
year = {2022}
}