$2$-Adic Complexity of Binary $m$-Sequences
Tian Tian, Wen‐Feng Qi · IEEE Transactions on Information Theory · 2010
Although 2 -adic complexity was proposed more than ten years ago, even form-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 binarym-sequence, its 2-adic complexity attains the maximum, which implies that no feedback with carry shift registers (FCSRs) with connection integer less than22n-1- 1 can generatem-sequences of ordern.