ZHENG Qunxiong, QI Wenfeng. The Unique Distribution of Zeros in CompressingSequences Derived from Primitive Sequencesover Z=(pe)[J]. Chinese Journal of Electronics, 2010, 19(1): 159-164.
Citation: ZHENG Qunxiong, QI Wenfeng. The Unique Distribution of Zeros in CompressingSequences Derived from Primitive Sequencesover Z=(pe)[J]. Chinese Journal of Electronics, 2010, 19(1): 159-164.

The Unique Distribution of Zeros in CompressingSequences Derived from Primitive Sequencesover Z=(pe)

  • Received Date: 1900-01-01
  • Rev Recd Date: 1900-01-01
  • Publish Date: 2010-01-05
  • 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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