ZHENG Qunxiong and QI Wenfeng, “The Unique Distribution of Zeros in CompressingSequences Derived from Primitive Sequencesover Z=(pe),” Chinese Journal of Electronics, vol. 19, no. 1, pp. 159-164, 2010,
Citation:
ZHENG Qunxiong and QI Wenfeng, “The Unique Distribution of Zeros in CompressingSequences Derived from Primitive Sequencesover Z=(pe),” Chinese Journal of Electronics, vol. 19, no. 1, pp. 159-164, 2010,
ZHENG Qunxiong and QI Wenfeng, “The Unique Distribution of Zeros in CompressingSequences Derived from Primitive Sequencesover Z=(pe),” Chinese Journal of Electronics, vol. 19, no. 1, pp. 159-164, 2010,
Citation:
ZHENG Qunxiong and QI Wenfeng, “The Unique Distribution of Zeros in CompressingSequences Derived from Primitive Sequencesover Z=(pe),” Chinese Journal of Electronics, vol. 19, no. 1, pp. 159-164, 2010,
Let Z=(pe) be the integer residue ring with odd prime p and integer e ¸ 3. Any sequence a over Z=(pe) has a unique p-adic expansion a = a0+a1 ¢p+¢ ¢ ¢+ae¡1 ¢pe¡1, where ai can be regarded as a sequence over Z=(p) for 0 · i · e ¡ 1. Let f(x) be a strongly primitive polynomial over Z=(pe) and let a; b be two primitive sequences gener- ated by f(x) over Z=(pe). Assume '(x0; ¢ ¢ ¢ ; xe¡1) = xe¡1 + ´(x0; ¢ ¢ ¢ ; xe¡2), where the degree of xe¡2 in ´(x0; ¢ ¢ ¢ ; xe¡2) is less than p¡1. It is shown that if '(a0(t); ¢ ¢ ¢ ; ae¡1(t)) = 0 if and only if '(b0(t); ¢ ¢ ¢ ; be¡1(t)) = 0 for all nonnegative integer t with ®(t) 6= 0, where ®, is an m-sequence de- termined by f(x) and a0, then a = b. In particular, when ´(x0; ¢ ¢ ¢ ; xe¡2) = 0, it is just the former result on the unique distribution of zeros in the highest level sequences.
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