WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
Symmetric 2-Adic Complexity of Generalized Cyclotomic Sequences with Period $$2p^{n}$$
Authors: , , ,
Abstract: Using the cyclotomic classes and generalized cyclotomic classes for sequence design is a well known method. In this paper, we study the symmetric 2-adic complexity of sequences based on generalized cyclotomic classes of order two. These sequences with period $$2p^{n}$$ have high linear complexity. We show that the 2-adic complexity of these sequences is good enough to resist the attack of the rational approximation algorithm. The 2-adic complexity is the measure of the predictability of a sequence which is important for cryptographic applications. Our method of studying 2-adic complexity is based on using the generalized “Gauss periods”.
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Keywords: Binary Sequence, 2-Adic Complexity, Cyclotomy, Generalized Cyclotomic Sequence, Gauss Period, Symmetric 2-Adic Complexity
Pages: 300-306
DOI: 10.37394/23206.2025.24.29