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自从Calderbank等人建立了从经典纠错码构造量子纠错码的CRSS构造法以来,人们利用经典纠错码构造了大量的性能良好的量子纠错码,称为量子稳定子码.最近的物理实验表明,大多数量子力学系统中发生量子比特翻转错误的概率远小于量子相位翻转错误的概率,针对这一情况所构造的纠错码称为非对称量子纠错码.本文分别基于嵌套包含Goppa码与对偶包含Goppa码构造了一系列新的非对称量子稳定子码.在基于嵌套包含Goppa码构造非对称量子码时,首先对Goppa码的选取做一定的限制,以便解析构造量子码.对于一般情况下的构造,则是借助于数学软件Matlab计算Goppa码对偶码的最小距离进行的.在基于对偶包含Goppa码的构造中,所构造量子码的纠错能力主要体现在纠正Z类型错误上.
Since Calderbank et al. Established the CRSS method of constructing quantum error correction codes from classical error correction codes, a large number of good quantum error correction codes have been constructed using classical error correction codes, called quantum stable subcodes.The nearest physical Experiments show that the probability of quantum bit flip error in most quantum mechanics systems is far less than the probability of quantum phase flip error, and the error correction code constructed in this case is called asymmetric quantum error correction code.In this paper, Goppa code and dual Goppa code construct a series of new asymmetric quantum stable sub-codes. When constructing non-symmetric quantum codes based on nested Goppa codes, we first make some restrictions on the selection of Goppa codes in order to resolve the construction of quantum codes For the general construction, the minimum distance of the Goppa code to the dual code is calculated by means of mathematic software Matlab.In the construction based on the dual-inclusive Goppa code, the error correction ability of the constructed quantum code mainly manifests itself in correcting the Z type Wrong.