Combinatoric collaboration on Costas arrays and radar applications

Costas arrays are permutation matrices that also provide a frequency indexing sequence that permits at most one coincident tone in cross-correlations of FSK waveforms. As such, they have obvious application as frequency indexing sequences in radar and communications when long codes with bounded autocorrelation are required or when Doppler is a significant portion of the transmitted bandwidth. All Costas arrays for orders less than 25 are known, with those for N=24 disclosed in the paper. Higher orders are found through number-theoretic generators and partial searches.