  Construction of quantum codes and entanglement-assisted quantum codes with
good parameters via classical codes is an important task for quantum computing
and quantum information. In this paper, by a family of one-generator
quasi-cyclic codes, we provide quasi-cyclic extended constructions that
preserve the self-orthogonality to obtain stabilizer quantum codes. As for the
computational results, some binary and ternary stabilizer codes with good
parameters are constructed. Moreover, we present methods to construct
maximal-entanglement entanglement-assisted quantum codes by means of the class
of quasi-cyclic codes and their extended codes. As an application, some good
maximal-entanglement entanglement-assisted quantum codes are obtained and their
parameters are compared.
