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2 -Adic Complexity of Binary m -Sequences

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2 Author(s)
Tian Tian ; Dept. of Appl. Math., Zhengzhou Inf. Sci. & Technol. Inst., Zhengzhou, China ; Wen-Feng Qi

Although 2 -adic complexity was proposed more than ten years ago, even for m -sequences which are thought of as the most important linear recurring sequences, no theoretical results about their 2-adic complexity has been presented. In this paper, it is shown that for a binary m-sequence, its 2-adic complexity attains the maximum, which implies that no feedback with carry shift registers (FCSRs) with connection integer less than 2 2 n -1 - 1 can generate m-sequences of order n .

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IEEE Transactions on Information Theory  (Volume:56 ,  Issue: 1 )