The Average Hamming Correlation for the Cubic Polynomial Hopping Sequences

The average Hamming correlation is an important performance indicator of the frequency hopping sequences. In this paper, the lower bound on the average Hamming correlation for frequency hopping sequences with respect to the size q of the frequency slot set, the sequence length L, the family size M, the average Hamming autocorrelation A_a and the average Hamming crosscorrelation A_c is established. The average Hamming correlation for the cubic polynomials hopping sequences over a finite field GF(p) is also derived and discussed. It is shown that the cubic polynomials hopping sequences over a finite field GF(p) are the optimal average Hamming correlation sets.