Zpe上本原序列的元素分布(英文)

Distribution of Elements in Primitive Sequences over Zpe

中文关键词:  环上本原序列  元素分布  指数和

英文关键词:primitive sequence over ring  element distribution  character sum

中文摘要:

      文研究了Z_p^e上本原序列的元素分布。利用Galois环上的指数和估计和本原序列的迹表示,得到了Z_p^e中各元素在本原序列的一个周期中出现频率的一个估计。当n>4e时(n为本原序列生成多项式的次数),我们的估计优于Kuzmin的结果。

英文摘要:

      Using the estimates of character sums over Galois rings and the trace de- scription of primitive sequences over Z_p^e, we obtain an estimate for the frequency of the occurrences of any element in Z_p^e in one period of a primitive sequence, which is better than Kuzmin's results if n >4e, where n is the degree of the generating polynomial of the primitive sequence.