【摘要】 作者提出了移位寄存器循环序列(又称为圈)应分为质圈和复合圈的概念。又证明了n级移位寄存器的全部质圈就是n-1级移位寄存器的全部圈。在分析质圈和复合圈的各种性质的基础上,提出了两种构造移位寄存器全部序列,即全部圈的方法:质圈合并法和M圈分离法。用这两种方法可以构造出目前还没有有效方法构造出的n=5的全部移位寄存器序列。结果表明n=5的序列(圈)共有30176个。这些结果已储存在计算机的软盘中,占900K的存贮空间。并用各种方法验证了它们的正确性。各种长度的循环序列的总数,已列成表附在文中。并用二进制码将各种序列打印成表,合计300页,以备选用。更多还原

【Abstract】 Although the advantages of nonlinear shift resister sequences over linearones are obvious, the structure of such sequences, until recently, has beenlittle understood, because of the complexity of this structure and the lack ofeffective methods to analyze them [1] [2] [3]. Many scholars have exerted great effort to gain an understanding of thisstructure, but they have obtained only all 179 sequences of 4-stage register [3]and all M sequences [6] [7]. In this paper, a new concept about shift resister sequences is advanced;it is believed to be a large advance in this difficult area, for example, byusing this new concept we find that there are 30176 cycles in 5-stase binaryshift registers. The above-mentioned new concept is essentially that we regard that shiftregister sequences (cycles) can be divided into two groups: group of primecycles and group of composite cycles. The prime cycles have many interestingproperties. Based on this new concept and by use of these properties, twonew methods of finding all possible sequences are established. They are"Joining the Prime Cycles method" and "Separating the M Cycles method". The author has stored the results of all possible cycles of 5-stage registersin computer and can supply the "Data Diskette" to user, in which all data ofcycles from length L=1 to L=32 are copied.更多还原