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Further Result on Distribution Properties of Compressing Sequences Derived From Primitive Sequences Over {\bf Z}/(p^{e})

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3 Author(s)
Qun-Xiong Zheng ; State Key Lab. of Math. Eng. & Adv. Comput., Zhengzhou Inf. Sci. & Technol. Inst., Zhengzhou, China ; Wen-Feng Qi ; Tian Tian

Let p be an odd prime number, e an integer greater than 1, and Z/(pe) the integer residue ring modulo pe. In this paper, we obtain an improved result of the previous paper (IEEE Trans. Inf. Theory, 56(1) (2010) 555-563) on distribution properties of compressing sequences derived from primitive sequences over Z/(pe). It is shown that two primitive sequences α and b generated by a strongly primitive polynomial f(x) over Z/(pe) are the same, if there exist s∈ Z/(p) and k∈ Z(p)* such that the distribution of in their compressing sequences ae-1+η(a0,⋯.ae-2) and be-1+η(b0,⋯,be-2) is coincident at the positions t with α(t)=k, where η(x0,⋯,xe-2) is an (e-)-variable polynomial over Z/(p) with the coefficient of xe-2p-1⋯x1p-1x0p-1 not equal to (-1)e · (p+1)/2 and α is an m-sequence over Z/(p)determined by f(x) and a. Compared with the previous result, this gives a more precise characterization on the positions of a compressing sequence, i.e., of the form ae-1+η(a0,⋯,ae-2), derived from a primitive sequence a over Z/(pe) that completely determines a. In particular, the result is also true for the highest level sequence ae-1 by taking η(x0,⋯,xe-2)=0.

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Information Theory, IEEE Transactions on  (Volume:59 ,  Issue: 8 )