Generalised class of cubic frequency-hopping sequences with large family size

Based on the cubic polynomials over finite field a generalised class of cubic frequency-hopping sequences with large family size suitable for applications in time/frequency hopping CDMA systems, multiuser radar and sonar systems is proposed and investigated. It is shown that the new time/frequency hopping sequences have at most two hits in their autocorrelation functions and at most three hits in their crosscorrelation functions except for a special case, and their family size is much larger than the conventional cubic hopping sequences. To estimate the influence of the special case the probability of the occurrence of the special case is calculated. In addition, as an important performance measure, the average number of hits for the generalised cubic hopping sequences is also derived and discussed.