In order to overcome the shortcomings as high computational complexity and low fault tolerance in recognition of cyclic code by the hard-dicision algorithms

a algorithm based on soft-decision is proposed. Firstly

based on the structure of coding algebra

it is deduced that the dual space corresponding to the polynomial factor are orthogonal to the codeword space. Secondly

based on the deduced conclusion

the possible length of code is traversed

then the polynomial

x

n

+1 is decomposed into the product of irreducible factors and their powers

when the dual space of the

traversing factor coincides with the parity-check of the code word sequence

the length can be recognized. Finally

by traversing the polynomial factors and the corresponding power

the generated polynomial can be identified. In addition

the concept of average checking conformity is introduced in parity-check matching. Based on its statistical property and minimum error decision criterion

the fast identification of generating polynomial factor and power is completed. The simulation results show that the derived statistical property are consistent with the actual situation

and at the same time

the proposed algorithm has better performance in low SNR

which can achieve over 95% of correct recognition rate in 3dB noise environment. Compared with the existing methods

although it increases the computational complexity slightly

its performance improved by nearly 1dB. It has a good application prospect in intelligent communication or cognitive radio.