DocumentCode :
1062037
Title :
Injectivity of Compressing Maps on Primitive Sequences Over Z/(pe)
Author :
Tian, Tian ; Qi, Wen-Feng
Volume :
53
Issue :
8
fYear :
2007
Firstpage :
2960
Lastpage :
2966
Abstract :
Let Zopf/(pe) be the integer residue ring with odd prime p and integer eges2. For a sequence a_ over Zopf/(pe), one has a unique p-adic expansion a_=a_0+a_1.p+...+a_(e-1).pe-1, where a_i can be regarded as a sequence over Zopf/(p) for 0lesilese-1. Let f(x) be a strongly primitive polynomial over Zopf/(pe) and G´(f(x), pe) be the set of all primitive sequences generated f(x) by over Zopf/(pe). Recently, the authors, Xuan-Yong Zhu and Wen-Feng Qi, have proved that for a function phi(x0,...,xe-1)=g(xe-1)+eta(x0,...,xe-2)over Zopf/(p) and a_,b_isinG´f(x),pe), where 2lesdeg glesp-1, phi(a_0,a_1...,a_e-1)=phi(b_0,b_1...,b_e-1) if and only if a_=b_. To further complete their work, we show that such injectivity also holds for deg g=1. That is for a function phi(x0,...,xe-1)=xe-1+eta(x0,...,xe-2)over Zopf/(p) and a_,b_isinG´f(x),pe), phi(a_0,a_1...,a_e-1)=phi(b_0,b_1...,b_e-1) if and only if a_=b_.
Keywords :
cryptography; data compression; number theory; sequences; compressing maps; integer recurring sequence; integer residue ring; primitive sequence; Decoding; Degradation; Information theory; Notice of Violation; Rate-distortion; Reliability theory; Source coding; Testing; Compressing map; integer residue ring; linear recurring sequence; primitive sequence;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2007.901214
Filename :
4276940
Link To Document :
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