The 2-adic complexity of a class of binary sequences with almost optimal autocorrelation

Pseudo-random sequences with good statistical property, such as low autocorrelation, high linear complexity and large 2-adic complexity, have been used in designing reliable stream ciphers. In this paper, we obtain the exact autocorrelation distribution of a class of sequence with three-level autocorrelation and analyze the 2-adic complexity of this sequence. Our results show that the 2-adic complexity of the sequence is at least (N + 1) − log 2 (N + 1) and that in many cases it is maximal, which is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).