In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of $1$-generator QC codes and their symplectic dual codes by decomposing code spaces. As an application, we construct numerous new binary symplectic self-orthogonal QC codes with excellent parameters, leading to $117$ record-breaking quantum error-correction codes.

翻译：本文建立了指数为偶数的准循环码成为辛自正交的充分必要条件。随后，通过分解码空间，我们给出了一类单生成元准循环码及其辛对偶码的最小辛距离的上下界。作为应用，我们构造了大量具有优异参数的新二元辛自正交准循环码，从而得到了117个破纪录的量子纠错码。