Abstract: A class of differential frequency hopping (DFH) codes based on the recursive shift register is designed. The path weight distribution and the distance spectrum of the DFH codes are defined. The fast algorithm for the two parameters is given. The upper bound of the Viterbi detection algorithm performance for DFH system is derived by using two different methods. Simulation results indicate that the performance evaluation of the bit error rate (BER) given by the upper bound is accurate, when the hopping set includes 8 frequencies and the BER is less than 10^-3. Finally the rules to select the good codes of the DFH codes are given.