构造长度为 $ 4p^{s} $ 的量子重根循环码

文章研究 $ F_{p^{m}} $ 上码长是 $ 4p^{s} $ 重根循环码的对偶包含性;基于重根循环码的代数结构,给出 $ F_{p^{m}} $ 上码长是 $ 4p^{s} $ 重根循环码是对偶包含码的充要条件,并确定了它们的最小距离;基于 Steane 扩展构造,构造了几类参数较好的非二元量子码。

In this paper, the repeated-root cyclic codes of length $ 4p^{s} $ over $ F_{p^{m}} $ which contain their dual codes are studied. Based on algebraic structure of the repeated-root cyclic codes, a necessary and sufficient condition for the repeated-root cyclic codes of length $ 4p^{s} $ over $ F_{p^{m}} $ which contain their dual codes is given, and their minimum distance is determined. Based on Steane's enlargement construction, several kinds of non-binary quantum codes with better parameters are constructed.