Galois FCSR的内部状态分析  

Inner State Analysis of Galois FCSR

作　　者：薛帅[1] 戚文峰[1] 

机构地区：[1]解放军信息工程大学应用数学系,郑州450002

出　　处：《计算机工程》2008年第18期179-180,183,共3页Computer Engineering

基　　金：国家自然科学基金资助项目(60673081);国家"863"计划基金资助项目(2006AA01Z417)

摘　　要：研究Galois FCSR状态序列的周期与互补性质及进位序列的互补性质。根据周期序列与有理数2-adic表达之间的关系，证明l-序列的状态序列是准周期的，且其周期与l-序列的周期相同。分析以q为极小连接数的l-序列a的状态序列s=（s0，s1，…，sn）及进位序列c=（c0，c1,…，cn），证明若s在t时刻进入周期，则i≥t时，si＋si＋T/2=∑j=0^r-12^j，ci＋ci＋T/2=q-∑j=0^r-12^j，其中，T=per（a），r=[1b（q＋1）]。This paper investigates the period and complementarity property of Galois FCSR state-sequence, and the complementarity proterty of carry-sequence as well. By analyzing the relationship between a periodic sequence and the 2-adic expansion of a rational number, it is proved that the state-sequence of an l-sequence is eventually periodic and has the same period as that of the l-sequence. It analyzes an l-sequence a with minimum connection integer q, state-sequence s=（s0, s1,…, sn） and carry-sequence c=（c0, c1,…, cn）, and proves that si＋si＋T/2=∑j=0^r-12^j,ci＋ci＋T/2=q-∑j=0^r-12^j for i≥t, where T= per（a）, r = [1b（q＋1）], and t is the time after which s is strictly periodic.

关 键 词：同期互补序列 状态序列 进位序列 

分 类 号：TP311.12[自动化与计算机技术—计算机软件与理论]