四元码链和量子纠错码的构造

Quaternary Self-orthogonal Code Chains and Construction of Quantum Error-correcting Codes

研究量子纠错码的构造,并构造出具有较好参数的量子纠错码。首先利用随机搜索的方法,得到一些具有较好参数的短码长自正交码及由这些自正交码所形成的自正交码链;其次根据这些自正交码的对偶码可得到一系列相应参数的L-链;最后通过组合构造方法和得到的这些L-链构造出量子纠错码。得到一些码长n满足20≤n≤36和n=40,45,50,55,60、对偶距离达到5或6的自正交码,并根据这些自正交码和它们的对偶码分别构造出了相应参数的自正交码链及L-链。构造出具有较好参数的量子纠错码,其中码长在20≤n≤30范围内的量子纠错码的参数达到或超过了已知的量子纠错码,码长在31≤n≤36和40≤n≤64范围内的量子纠错码都是新的。

The method of constructing quantum error - correcting code by the quaternary self - orthogonal sub - code chains and L - chains are investigated in this paper. Random searching method is used to find quaternary self - orthogonal codes and these self- orthogonal codes could form some self - orthogonal code chains. By using com- binatorial method, quantum error - correcting codes are constructed in light of L - chains which are constructed by dual of these self - orthogonal codes. The code chains of these self - orthogonal sub - codes and the L - chains which are obtained from the dual of these self - orthogonal sub - codes of length n between 20 and 36 and n = 40, 45,50,55,60 and dual distance five and six are determined. Some quantum codes of distance five and six are constructed by the obtained L - chains, some quantum error - correcting codes are new.