Frequency hop multiple access codes based upon the theory of cubic congruences

The need for families of frequency-hop codes which have mutually small auto-ambiguity and cross-ambiguity functions is discussed. Current coding methods are reviewed. A new family of frequency-hop codes based upon the number-theoretic concept of cubic congruences is introduced. It is shown that for about 50% of the prime numbers, families of full codes exist which have at most two coincidences for any time-frequency shift in their auto-ambiguity functions and at most three coincidences in the set of mutual cross-ambiguity functions