On the Maximal Cross-Correlation of Algebraically Constructed Costas Arrays

Families of Costas arrays with low pairwise cross-correlation are sought. The two families of all exponential Welch arrays and all Golomb arrays generated in a certain finite field are specifically studied, and the maximal cross-correlation is determined by exhaustive search. Mathematically rigorous explanations for some of the observed results are presented, a surprising link between Welch and Golomb arrays is revealed, and what remains to be proved is stated precisely. The results suggest that the families with uniformly low cross-correlation correspond to finite fields whose size is a safe prime power.