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In this paper, a new method is presented to compute the 2-adic complexity ofpseudo-random sequences. With this method, the 2-adic complexities of all theknown sequences with ideal 2-level autocorrelation are uniformly determined.Results show that their 2-adic complexities equal their periods. In otherwords, their 2-adic complexities attain the maximum. Moreover, 2-adiccomplexities of two classes of optimal autocorrelation sequences with period$N\equiv1\mod4$, namely Legendre sequences and Ding-Helleseth-Lam sequences,are investigated. Besides, this method also can be used to compute the linearcomplexity of binary sequences regarded as sequences over other finite fields.

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