A New Method to Compute the 2-Adic Complexity of Binary Sequences

In this paper, a new method is presented to compute the 2-adic complexity of pseudo-random sequences. With this method, the 2-adic complexities of all the known sequences with ideal 2-level autocorrelation are determined in a unified way. Results show that their 2-adic complexities equal their periods. In other words, their 2-adic complexities attain the maximum. In addition, 2-adic complexities of two classes of optimal autocorrelation sequences with period N ≡ 1mod4, namely Legendre sequences and Ding-Helleseth-Lam sequences, are investigated. This method also can be used to compute the linear complexity of binary sequences regarded as sequences over other finite fields.