A New Method to Compute the 2-adic Complexity of Binary Sequences
This work addresses a specific problem in cryptography and coding theory for researchers, providing incremental improvements in analyzing pseudo-random sequences.
The paper tackles the problem of computing the 2-adic complexity of binary sequences, presenting a new method that uniformly determines these complexities for all known sequences with ideal 2-level autocorrelation, showing they equal their periods and thus attain the maximum.
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 uniformly determined. Results show that their 2-adic complexities equal their periods. In other words, their 2-adic complexities attain the maximum. Moreover, 2-adic complexities 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 linear complexity of binary sequences regarded as sequences over other finite fields.