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

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