计算几类周期序列的最小周期

在流密码中，周期序列的周期是一个重要指标。在周期序列的线性复杂度相同的情况下，序列的最小周期越大越好。我们证明，如果由一个非退化组合函数Fn所组合的n个周期序列的”个最小周期两两互素，则由Fn所产生的输出序列的最小周期达到最大值。笔者推出的另一个好的主要的结果是，如果由一个非退化组合函数Fn所组合的n个GF（2）上最大长度线性反馈移位寄存器的长度是不同的且大于2，则由Fn所产生的输出序列的最小周期也达到最大值。最后我们给山一个后例，它表明第二个结果对非二元域不成立。

Least Periods Computing of Some Classes of Periodic Sequences

In stream cipher, the period of periodic sequence is an important measure. Under the condition that linear complexities of periodic sequences are equal, the larger the least periods of these sequences, the better. It is proved that if n least periods of nperiodic sequences combined by a non-degenerate combining function Fn are pairwise relatively prime, the least period of the output sequence produced by Fnattains maximal value.Another principal result derived in this paper is that if the lengths ofnmaximum-length GF（2） LFSR＇ s combined by a non degenerate combining function Fn are different and greater than two, the least period of the output sequence produced by Fnalso attains maximal value. Finally, an example shows that the second result is not true for non-binary fields.