The nonlinear complexity of level sequences over Z/(4) |
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Institution: | 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: | For any sequence over , there is an unique 2-adic expansion , where and are sequences over and can be regarded as sequences over the binary field naturally. We call and the level sequences of . Let be a primitive polynomial of degree over , and be a primitive sequence generated by . In this paper, we discuss how many bits of can determine uniquely the original primitive sequence . This issue is equivalent with one to estimate the whole nonlinear complexity, , of all level sequences of . We prove that is a tight upper bound of if is a primitive trinomial over . Moreover, the experimental result shows that varies around if is a primitive polynomial over . From this result, we can deduce that is much smaller than , where is the linear complexity of level sequences of . |
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