论文标题
符号自动式准循环代码
Symplectic self-orthogonal quasi-cyclic codes
论文作者
论文摘要
在本文中，我们建立了具有索引的准循环（QC）代码的必要条件，甚至是符合性的自动性。随后，我们通过分解代码空间的$ 1 $生成器QC代码的类别的最小符号距离及其符号双重代码介绍了下层和上限。作为一个应用程序，我们构建了具有出色参数的许多新的二进制符号自动QC代码，从而导致$ 117 $创纪录的量子误差校正代码。
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.
