Abstract: 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  , ci  ci  T/2  q for i≥t, where T = per(a), r = lb(q+1), and t is the time after which s is strictly periodic.

Key words: periodic complementary sequence, state-sequence, carry-sequence

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  , ci  ci  T/2  q ，其中，T = per(a), r = lb(q+1)。

关键词: 周期互补序列, 状态序列, 进位序列

CLC Number: 

• TP311.12