In this paper, we obtain the necessary and sufficient conditions for quasi-cyclic codes with index even to be symplectic self-orthogonal. Then, we propose a method for constructing symplectic self-orthogonal quasi-cyclic codes, which allows arbitrary polynomials that divide $ x^{n}-1$ to construct symplectic self-orthogonal codes. Especially in the case of $1$-generator quasi-cyclic codes with index two, our construction improves Calderbank's additive construction, Theorem 14 in ``Quantum error correction via codes over $GF(4)$". Finally, we construct many binary symplectic self-orthogonal codes with excellent parameters to illustrate our approach's effectiveness. The corresponding quantum codes improve Grassl's table (bounds on the minimum distance of quantum codes. http://www.codetables.de).
翻译：在本文中,我们为具有指数的准周期代码获得了必要和充分的条件,即使指数是相互跳动的自我垂直的。 然后,我们提出了一种方法,用于构建相互跳动的自我垂直准周期代码。 这种方法允许任意的多民族代码分割 x ⁇ n}-1美元,用于构建相互跳动的自我垂直代码。 特别是,对于具有指数2的1美元生成的准周期代码,我们的建筑改进了卡尔德银行的添加剂结构,“ 单子” 14 的理论,通过超过$GF(4)$的代码来纠正“ 子” 。 最后,我们构建了许多二进式的自我垂直代码,有极好的参数来说明我们的方法的有效性。 相应的量子代码改善了格拉特尔的表格(距离最小量子代码的边距)。 http://www.codebables.de)。
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