Abstract: A linear scrambler was usually defined based on a linear feedback shift register (LFSR). An eavesdropper must reconstruct the scrambler of the communication scheme to recover the information sequence. In order to effectively solve the problem of the applicability of the scrambler reconstruction, the performance of an algorithm based on WalshHadamard transformation is theoretically studied, and the related factors affecting the algorithm are analyzed. Firstly, we express the misjudgment probability as a function of the amount of  received  data, the bias of information sequence and the weight of feedback polynomial. Secondly, when a misjudgment probability is given, we analyze the required amount of received data to meet the performance demand. Finally, we discuss the algorithm complexity. This work provides a theoretical basis for engineering applications and further studies on the reconstruction of linear scrambler.