构造长度为4p^(s)的量子重根循环码

Structure of quantum repeated-root cyclic codes of length 4p^(s)

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.