On the distinctness of modular reductions of maximal length sequences modulo odd prime powers |
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| Authors: | Xuan-Yong Zhu Wen-Feng Qi. |
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| 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 ; Department of Applied Mathematics, Zhengzhou Information Engineering University, P.O. Box 1001-745, Zhengzhou, 450002, People's Republic of China |
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| Abstract: | We discuss the distinctness problem of the reductions modulo  of maximal length sequences modulo powers of an odd prime  , where the integer  has a prime factor different from  . For any two different maximal length sequences generated by the same polynomial, we prove that their reductions modulo  are distinct. In other words, the reduction modulo  of a maximal length sequence is proved to contain all the information of the original sequence. |
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| Keywords: | Integer residue ring linear recurring sequence primitive polynomial primitive sequence modular reduction |
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