In this paper, we obtain sufficient and necessary 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 coprime $x^{n}-1$ to construct symplectic self-orthogonal codes. Moreover, by decomposing the space of quasi-cyclic codes, we provide lower and upper bounds on the minimum symplectic distances of a class of 1-generator quasi-cyclic codes and their symplectic dual codes. Finally, we construct many binary symplectic self-orthogonal codes with excellent parameters, corresponding to 117 record-breaking quantum codes, improving Grassl's table (Bounds on the Minimum Distance of Quantum Codes. http://www.codetables.de).

翻译：本文给出了偶数指标准循环码为辛对称自正交的充要条件。随后提出了一种构造辛对称自正交准循环码的方法，该方法允许利用任意与$x^{n}-1$互素的多项式来构建辛对称自正交码。进一步地，通过对准循环码空间进行分解，我们为一类单生成元准循环码及其辛对偶码的最小辛距离提供了上下界。最后，我们构造了大量具有优异参数的二元辛对称自正交码，这些码对应117个破纪录的量子码，改进了Grassl表（《量子码最小距离界》，http://www.codetables.de）。