Determination of the Autocorrelation Distribution and 2-Adic Complexity of Generalized Cyclotomic Binary Sequences of Order 2 with Period pq

05/23/2021

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by   Xiaoyan Jing, et al.

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The generalized cyclotomic binary sequences S=S(a, b, c) with period n=pq have good autocorrelation property where (a, b, c)∈{0, 1}^3 and p, q are distinct odd primes. For some cases, the sequences S have ideal or optimal autocorrelation. In this paper we determine the autocorrelation distribution and 2-adic complexity of the sequences S=S(a, b, c) for all (a, b, c)∈{0, 1}^3 in a unified way by using group ring language and a version of quadratic Gauss sums valued in group ring R=ℤ[Γ] where Γ is a cyclic group of order n.