Symmetric 2-Adic Complexity of Generalized Cyclotomic Sequences with Period 2p^n

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”.