2-Adic Complexity of Binary m-Sequences
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(2n-1) - 1 can generate m-sequences of order n.
2-adic complexity m-sequences feedback with carry shift register (fcsr) sequences