Costas array generation and search methodology

Costas arrays are permutation matrices that provide sequencing schemes for frequency hop in FSK waveforms. Such frequency-shift keying (FSK) waveforms can be designed to have nearly ideal ambiguity function properties in both the time and frequency directions: the Costas property permits at most one coincident tone in autocorrelations in both time and frequency. Costas arrays are found by number-theoretic generators and their extensions, and by exhaustive search methods. Two new extensions of number-theoretic methods are introduced here that find two new Costas arrays. All Costas arrays for orders 24, 25, and 26 are disclosed here, including previously unknown examples.