Structural properties of Costas arrays

Abstract

We apply combinatorial arguments to establish structural constraints on Costas arrays. We prove restrictions on when a Costas array can contain a large corner region whose entries are all 0. In particular, we prove a 2010 conjecture due to Russo, Erickson and Beard. We then constrain the vectors joining pairs of 1s in a Costas array by establishing a series of results on its number of “mirror pairs,” namely pairs of these vectors having the same length but opposite slopes.

DOI: 10.3934/amc.2014.8.241

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Cite this paper

@article{Jedwab2014StructuralPO, title={Structural properties of Costas arrays}, author={Jonathan Jedwab and Jane Wodlinger}, journal={Adv. in Math. of Comm.}, year={2014}, volume={8}, pages={241-256} }