有限域上线性递归序列簇及其周期性(英文)

ON PERIODICITY AND FAMILIY OF LINEARLY RECURSIVE SEQUENCES OVER FINITE FIELDS

本文首次使用了HOPF代数的方法，研究了有限域F_q上线性递归序列问题，主要的结果如下：（1）有限域F_q上每一个线性递归序列都是终归周期的（ultimatelyperiodic）．（2）S（f（x））=（f（x））．此外，我们还推广和化简了［5］中许多工作。你将发现这种方法比较方便、自然，而且值得进一步探讨。

篧e study the linearly recursive over finite fields F_q by the methods of Hopfalgebras. Main results are as follows: (1) Every linearly recursive over F_q isultimately periodic. (2) S(f(x) )= (f(x) . In addition,many works of[5] are generalized and simplied. One may find this methods moreconvienient,more natural, and worth further investigating.