Abstract: To suppress the existence of qubit decoherence effectively in quantum information processing, a construction method for nonbinary quantum error correcting codes based on cyclotomic coset is presented. Firstly, the related properties of cyclotomic coset are analyzed, and generator polynomial of BCH codes containing its Euclidean dual codes is determined. Using the Steane’s enlargement of Calderbank-Shor-Steane （CSS） constructions, these constructions generate new families of nonbinary quantum codes. The results show that the constructions for nonbinary quantum codes based on cyclotomic coset presented here have parameters better than the ones available in the literature.

Key words: cyclotomic cosets, Euclidean dual codes, quantum error correcting codes, Steane’s constructions, nonbinary quantum codes

摘要： 为了有效克服量子信息处理过程中存在的量子比特消相干，提出了一种基于分圆陪集非二进制量子纠错码的构造方法。分析了分圆陪集的相关性质，确定BCH码包含其Euclidean对偶码的生成多项式，利用扩展的Calderbank-
Shor-Steane（CSS）构造即Steane’s构造方法，构造出一批新的非二进制量子码。通过与已有的量子纠错码相比，结果表明，采用基于分圆陪集非二进制量子码构造方法构造的参数更优。

关键词: 分圆陪集, Euclidean对偶码, 量子纠错码, Steane&rsquo, s构造方法, 非二进制量子码