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On the distinctness of modular reductions of maximal length sequences modulo odd prime powers


Authors: Xuan-Yong Zhu and Wen-Feng Qi
Journal: Math. Comp. 77 (2008), 1623-1637
MSC (2000): Primary 11B50, 94A55
DOI: https://doi.org/10.1090/S0025-5718-08-02075-9
Published electronically: January 31, 2008
MathSciNet review: 2398784
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Abstract: We discuss the distinctness problem of the reductions modulo $ M$ of maximal length sequences modulo powers of an odd prime $ p$, where the integer $ M$ has a prime factor different from $ p$. For any two different maximal length sequences generated by the same polynomial, we prove that their reductions modulo $ M$ are distinct. In other words, the reduction modulo $ M$ of a maximal length sequence is proved to contain all the information of the original sequence.


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Additional Information

Xuan-Yong Zhu
Affiliation: China National Digital Switching System Engineering and Technological R&D Center (NDSC), P.O. Box 1001-783, Zhengzhou, 450002, People’s Republic of China
Email: xuanyong.zhu@263.net or zxy@mail.ndsc.com.cn

Wen-Feng Qi
Affiliation: Department of Applied Mathematics, Zhengzhou Information Engineering University, P.O. Box 1001-745, Zhengzhou, 450002, People’s Republic of China
Email: wenfeng.qi@263.net

DOI: https://doi.org/10.1090/S0025-5718-08-02075-9
Keywords: Integer residue ring, linear recurring sequence, primitive polynomial, primitive sequence, modular reduction
Received by editor(s): August 9, 2004
Received by editor(s) in revised form: May 24, 2007
Published electronically: January 31, 2008
Additional Notes: This work was supported by the National 863 Plan of China (Grant 2006AA01Z417) and the National Natural Science Foundation of China (Grant 60673081)
This paper is in final form and no version of it will be submitted for publication elsewhere.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.