A Method for Blind Recognition of Convolution Code Based on Euclidean Algorithm

The key equation (KE) plays an important role in cryptography and communication. In this paper, a new generalization of KE is introduced. By the problem of convolution code blind recognition, a multi-order key equation (MKE) is introduced. It is proved that the MKE can be used for blind recognition of convolution code with any code rate. A fast algorithm based on Euclidean algorithm is achieved which can solve 2-order KE. A new method for blind recognition of convolution code with 1/2 code rate is given, and an example is given in detail, then the computation load is analyzed. The computation load of our algorithm not more than L times N/2, where L is the length of the shortest linear feedback shift register to generate it, N is code length.