A search algorithm for bases of Calderbank-Shor-Steane type quantum error-correcting codes

Recently, Vatan, Roychowdhury and Anantram have presented two types of revi sed versions of the Calderbank-Shor-Steane code construction, and have also provided an exhaustive procedure for determining bases of quantum error-co rrecting codes. In this paper, we investigate the revised versions given by Vatan ct al., and point out that there is no essential difference between them. In addition, we propose an efficient algorithm for searching for base s of quantum error-correcting codes. The proposed algorithm is based on som e fundamental properties of classical linear codes, and has much lower comp lexity; than Vatan et at's procedure.