It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be symplectic dual-containing. Then, a new method for constructing binary quantum codes using symplectic dual-containing codes is proposed. As an application, we construct 8 binary quantum codes that exceed the best-known results. Further, another 36 new binary quantum codes are obtained by propagation rules, all of which improve the lower bound on the minimum distances.
翻译：众所周知,量子编码可以通过古典的共振双重含汞编码来构建,本文认为,一套由两种生成的准循环编码组成,并提出了足够条件,使这些编码具有共振双重含汞编码。然后,提出了使用共振双重含汞编码来构建二进制量编码的新方法。作为一种应用,我们建造了8种超过最已知结果的二进制量编码。此外,通过传播规则又获得了36种新的二进制量编码,所有这些都提高了最低距离的下限。
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