A class of binary sequences with period $2p$ is constructed using generalized cyclotomic classes, and their linear complexity, minimal polynomial over ${\mathbb{F}_{{q}}}$ as well as 2-adic complexity are determined using Gauss period and group ring theory. The results show that the linear complexity of these sequences attains the maximum when $p\equiv \pm 1(\bmod~8)$ and is equal to {$p$+1} when $p\equiv \pm 3(\bmod~8)$ over extension field. Moreover, the 2-adic complexity of these sequences is maximum. According to Berlekamp-Massey(B-M) algorithm and the rational approximation algorithm(RAA), these sequences have quite good cryptographyic properties in the aspect of linear complexity and 2-adic complexity.

翻译：使用通用环球类、线性复杂度、 $\mathb{F ⁇ q}$的最小多元性、 以及2- dic 复杂性, 使用高斯周期和组环理论来决定。 结果表明, 当$p\equiv\ pm 1\\ bmod~ 8美元时, 这些序列的线性复杂度达到最大值, 当$p\ equiv\ pm 1\\ bmod~ 8美元时, 当 $p\ equiv\ pm 3( \ bmod~ 8) 超过扩展域时, 等于 $p$+1} 。 此外, 这些序列的2- a dic 复杂性是最大的。 据 Berlekamp- Masssey (B- M) 算法和合理的近似算法(RAA), 这些序列在线性复杂度和 2- adi 复杂度方面具有相当好的加密特性 。