四元域上自对偶码的子码链

Subcode chains of quaternary self-dual code

利用构造性算法,对码长n介于10≤n≤20的四元自对偶码的子码进行了研究,构造出对偶距离为3、4、5或6子码的生成矩阵,得到了相应的自正交码。利用这些自对偶码及构造出的具有较好对偶距离的自正交子码构造出了码链,并且导出相应的L-链。最后作为对四元域上自对偶码的码链和L-链的一个应用,利用加性量子纠错码的构造方法构造出一些量子纠错码,其中一些码的参数改进了前人所得的结果。

By using construction arithmetic, the subcodes ofquatemary self-dual codes with code length 10 〈 n 〈 20 are studied and several self-orthogonal codes＇ matrixes with dual distance 3,4,5 and 6 are constructed. The series of the self-dual and self-orthogonal chains are constructed by these matrixes and the subcodes＇ L-chains with maximal dual distance are deduced. In the end, some quantum error correct codes are constructed by using these quaternary subcodes＇ L-chains and the construction theory of additive quantum error correct code. Some quantum error correct codes with good parameters are better than previously known.