Three challenges in Costas arrays

We present 3 open challenges in the field of Costas arrays. They are: a) the determination of the number of dots on the main diagonal of a Welch array, and especially the maximal such number for a Welch array of a given order; b) the conjecture that the fraction of Welch arrays without dots on the main diagonal behaves asymptotically as the fraction of permutations without fixed points and hence approaches 1/e, and c) the determination of the parity populations of Golomb arrays generated in fields of characteristic 2.