2-adic complexity of binary m-sequences

Authors:
Tian Tian;Wen-Feng Qi
Affiliations:
Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, China;Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou, China and State Key Laboratory of Information Security, Institute of Software, Chinese Academy ...
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

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 22n-1 - 1 can generate m-sequences of order n.