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Linear Recurring Sequence
Primitive Polynomial
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Distribution properties of compressing sequences derived from primitive sequences over Z/(p
Distribution properties of compressing sequences derived from primitive sequences over Z/(p,10.1109/TIT.2009.2034782,IEEE Transactions on Information
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Distribution properties of compressing sequences derived from primitive sequences over Z/(p
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Citations: 1
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QunXiong Zheng
,
WenFeng Qi
Let Z/(pe) be the integer residue ring with odd prime p and integer e ¿ 2. Any sequence a over Z/(pe) has a unique padic expansion a = a0 + a1 · p + ··· + ae1 · pe1, 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 a, b be two primitive sequences generated by f(x) over Z/(pe). Assume ¿(x0,..., xe1) = xe1 + ¿(x0,..., xe2) is an evariable function over Z/(p) with the monomial (p+1)/2 xe2 p1 ...x1 p1 not pearing in the expression of ¿(x0,x1,..., xe2). It is shown that if there exists an s ¿ Z/(p) such that ¿(a0(t),..., ae1 (t)) = s if and only if ¿(b0 (t),..., be1 (t)) = s for all nonnegative t with ¿(i) ¿ 0, where ¿ is an msequence determined by f(x) and a0, then a = b. This implies that for compressing sequences derived from primitive sequences generated by f(x) over Z/(pe), single element distribution is unique on all positions t with ¿(t) ¿ 0. In particular, when ¿(x0,x1,..., xe2) = 0, it is a completion of the former result on the uniqueness of distribution of element 0 in highest level sequences.
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 56, no. 1, pp. 555563, 2010
DOI:
10.1109/TIT.2009.2034782
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Citations
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A new result on the distinctness of primitive sequences over Z/(pq) modulo 2
QunXiong Zheng
,
WenFeng Qi
Journal:
Finite Fields and Their Applications  FFA
, vol. 17, no. 3, pp. 254274, 2011