  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.
