环Z/(p^e)上本原权位序列0元素分布的保熵性(Ⅱ)

UNIQUENESS OF THE DISTRIBUTION OFZEROES OF PRIMITIVE LEVEL SEQUENCESOVER Z/(pe)(Ⅱ)

设Re=Z/(3e)为整数模3e剩余类环, e≥2.环风Re上序列a有唯一的权位分解 ,其中ai是{0,1,2}上序列.称ai为a的第i权位序列,ae-1为a的最高权位序列.它们可自然视为Z/(3)上序列.设f(x)是Re上本原多项式,a和b是Re上由f(x)生成的序列,a≠0(mod3e-1),本文证明了最高权位序列 的0元素分布包含原序列a的所有信息,即,对所有非负整数t,若ae-1(t)=0当且仅当be-1(t)=0,则a=b.并由此得到: (i)两条不同的本原权位序列是线性无关的; (ii)任给正整数k,函数 是保熵函数,即对由f(x)生成的序列a和b,a=b当且仅当 (mod3).

et Re = Z/(3e) be the integer residue ring modulo 3e, e ≥ 2. For a sequence a over Re there is a unique decomposition a = a0 + a0-3 + … ae-1 · 3e-1, where ai is a sequence over {0,1,2}, and is called the i-th level sequence of a. Specially, ae-1 is called the highest level sequence of a. They can be considered as the sequence over Z/(3) naturally. Let f(x) be a primitive polynomial over Rea and 6 sequences generated by f(x) over Re a ≠0(mod 3e-1). It would be proved that the distribution of zeroes in the sequence ae-1 = (ae-1(t))t≥0 contains all the information of the original sequence a, that is, if ae-1(t) = 0 iff be-1(t) = 0 for all integer t ≥0, then a = b. Based on it, there are two results: (i) two differernt primitive level sequences are linear independent over Z/(3); (ii) for all positive integer k, a = b iff ae-1k = be-1k(mod3).