New coding schemes for increased number of users or messages in frequency-hopped multilevel FSK

The properties of four new frequency hop coding schemes are investigated. These schemes allow the maximum number of users (or messages) to be proportional to the square of the length of the code used in the system. They are based on n-th order congruences except that an additional term is introduced in the polynomial that defines the placement operator. The frequency difference function for each of these schemes is derived and analyzed, and the maximum number of hits in the auto- and cross-hit arrays is calculated. It is shown that there is only a slight increase in the number of hits as compared to the previous schemes.