中国剩余定理与剩余类环Z/(m)上的递归序列

The Chinese Remainder Theorem and the Recurring Sequences over Z/(m)

本文基于中国剩余定理给出了一种Z/(m)上递归序列极小多项式的求法和大周期的非线性递归序列的求法,并讨论了线性递归序列之极小多项式的个数,周期和圈数的下界等问题。

In this paper, two simple methods based on the Chinese remainder theorem are given, which can be used to find the minimum polynomials of the linear recurring sequences over Z/(m) and to find the non-linear recurring sequences with large periods. Then the number of the minimum polynomials and the lower bounds of the periods and the circlenumbers are discussed.