English

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}
}