Z/(2~e)上本原最高权位序列的随机性质

RANDOMNESS OF PRIMITIVE HIGHEST LEVEL SEQUENCE OVER Z/(2e)

本文研究环Z/（2e）上本原序列最高权位的0,1分布,证明了当e≥16,次数n≥20时,本原序列a的最高权位序列a_（e-1）在一个周期中0（或1）所占的比例λ（a_（e-1））满足45.2306％<λ（a_（e-1））<54.7694％.

Abstract In the paper we study the distribution of 0 and 1 in the highest level of primitive sequences. It is proved that the proportion λ(a_(e-1)) of 0 (or 1) in one period of a_(e-1) satisfies 45.2306%<λ(a_(e-1)) <54.7694% for e≥16 and n≥20.