A new family of frequency hopping patterns with good Hamming autocorrelation and crosscorrelation

A new family of frequency hopping patterns with long period and good Hamming autocorrelation and Hamming crosscorrelation properties which can be used for frequency hopped multiple access communication systems is introduced. Period of frequency hopping patterns is q^k - 1, the alphabet size of frequency hopping patterns is q where k is an arbitrary integer and q a is power of a prime number. The maximum value of out-of-phase Hamming autocorrelation function of any frequency hopping pattern and Hamming crosscorrelation function of any two frequency hopping patterns in the family is q^k-1, which corresponds to optimal Hamming correlation properties. Thus the average number of hits per q × q square in one frequency hopping pattern and its time shifted version or two frequency hopping patterns in the frequency hopped multiple access communication systems is less than 1