Ding constructed a new cyclotomic class V 0   , V 1 . Based on it, a construction of generalized cyclotomic binary sequences with period p q is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed. The autocorrelation function C S w is 3-level if p ≡ 3 mod 4 , and C S w is 5-level if p ≡ 1 mod 4 . The linear complexity LC S > p q / 2 if p ≡ 1   mod   8 , p > q + 1 , or p ≡ 3 mod 4 or p ≡ − 3 mod 8 . The results show that these sequences have quite good cryptographic properties in the aspect of autocorrelation and linear complexity.

A class of binary sequences with period pq is constructed using generalized cyclotomic classes, and their autocorrelation distribution and 2-adic complexity are determined using Gauss sum and group ring theory. The results show that the autocorrelation function of the new sequences is 3-level if p ≡ 3 (mod 4) and q ≡ 3 (mod 4) which is very close to the optimal and the 2-adic complexity of these sequences is maximum if p < q < 2p − 1. According to the rational approximation algorithm(RAA), these sequences have quite good cryptographic properties in the aspect of autocorrelation and 2-adic complexity.