标题：Nonsingularity of feedback shift registers
作者：Liu, Zhenbin; Wang, Yuzhen; Cheng, Daizhan
作者机构：[Liu, Zhenbin] Qingdao Agr Univ, Sch Sci & Informat Sci, Qingdao 266109, Peoples R China.; [Liu, Zhenbin; Wang, Yuzhen; Cheng, Daizhan] Shandong Uni 更多
关键词：Feedback shift register; Nonsingularity; Cycle; Decomposition and; synthesis; Semi-tensor product
摘要：In this paper, the multi-valued feedback shift register (FSR) is studied and a new approach is present to analyze its nonsingularity, number of cycles, and cycle synthesis. Firstly, the FSR is expressed in an algebraical form, based on which several necessary and sufficient conditions are given for the nonsingularity, Secondly, the structural matrix of FSR is defined, and a new method is introduced to determine the number of cycles with different lengths for arbitrarily given FSR. Thirdly, the problem on cycle decomposition and.synthesis of an FSR is investigated, and some new results are obtained. Finally, an illustrative example is studied to support our new results. (C) 2015 Elsevier Ltd. All rights reserved.