Recursive construction of optimal frequency-hopping sequence sets

In this study, first the authors present a simplified representation of the Peng-Fan bounds on the periodic Hamming correlation of frequency-hopping sequence (FHS) sets, which may also be used to check the optimality of an FHS set with respect to the Peng-Fan bounds. Second, they propose a recursive construction of FHS sets from the known ones using some injective functions and the Chinese remainder theorem. It generalises the previous construction of optimal FHSs and FHS sets with composite lengths employing a given function. Without the limit of the specific function, their construction can produce new optimal FHSs and FHS sets that cannot be produced by the earlier construction. By choosing appropriate injective functions and known optimal FHSs and FHS sets, infinitely many new optimal FHSs and FHS sets can be recursively obtained.