2-Adic complexity of Ding–Helleseth binary sequences with period pq - V. A. Edemskiy (Учёные записки Казанского университета: Серия Физико-математические науки, 2025)
A method is proposed to analyze the 2-adic complexity of generalized cyclotomic binary sequences with period pq. Along with linear complexity, 2-adic complexity serves as an important measure of sequence unpredictability. The method is based on generalized Gaussian periods of various orders using the prime modules p and q. The 2-adic complexity of Ding–Helleseth generalized cyclotomic sequences of orders two, four, and six with high linear complexity is estimated. The analysis shows that these sequences have high 2-adic complexity, which is sufficient to resist attacks using the rational approximation algorithm. Previous results obtained for the sequences of order two are summarized. The proposed method can be applied to a different type of sequences defined using generalized cyclotomic classes of various orders, as well as to investigate the m-adic complexity of both binary and non-binary sequences, such as quaternary sequences.