The construction and performance of frequency hopping codes were discussed but the emphasis was laid on the construction of Costas arrays.The frequency hopping codes called Costas arrays could be designed to have almost ideal auto-ambiguity and good cross-ambiguity.A mathematical model was established for frequency hop coded waveforms and the conditions for orthogonal sub-pulse were given.The auto-and cross-correlation properties of Costas arrays were illuminated

the practical properties of cross-correlation function of permutation matrices were revealed

the algorithms for computing ambiguity function were presented and the simulation results were demonstrated.After a study of the cross-ambiguity properties of Costas arrays the ways were suggested to reduce interference in a multiuser radar system.