Still More Structural Properties of Algebraic Costas Arrays

Costas arrays are fundamental to the operation of radar and sonar systems, yet it is still an open problem how to generate a Costas array for an arbitrary length. A way to improve computer search is to make use of a characterization of the structural properties in order to reduce the search space. In this work, we use techniques from uniform distribution theory to study several structural constraints on Welch and Golomb constructions of Costas arrays. Then, we find bounds on the number of streaks of a given length and their deficiency and test their tightness with several numerical experiments. These results partially answer questions posed by Correll, Jedwab, and Wodlinger.