In order to recognize the shortened Reed-Solomon(RS) code, a recognition method based on the Galois domain Fourier transform of arbitrary length is proposed. Firstly, the limited length of the Galois Field Fourier Transform(GFFT) is extended to any length, then the GFFT spectrum of the shortened RS code is calculated for different orders, primitive polynomial and code length, and the spectral cumulant is calculated; then the decision threshold value is determined according to the probability distribution of the spectral cumulant, and the decision is made so as to realize the identification of the coding parameters of the shortened RS code. The simulation results show that when the order is no more than 8 and the bit error rate is no more than 0.001, the correct recognition rate is no less than 99%.