摘要
循环陪集在经典和量子纠错编码理论中具有非常重要的作用.根据CSS编码定理知,利用经典BCH码构造量子BCH码时需要判断经典BCH码是否包含其对偶码.本文给出了循环陪集的若干重要性质,根据这些性质得到了判断有限域上非本原BCH码是否包含其对偶码的准则.本文给出的判断准则时间复杂度为多项式的,并且该判断准则对本原BCH码也适用.
Cyclotomic cosets play very important roles in classical and quantum error correction theory.In order to constructing quantum BCH（Bose Chaudhuri Hocquenghem） codes with CSS constructing method from classical BCH codes,it needs to determine whether a BCH code contains its dual.It proposed several properties of cyclotomic cosets.And according to these properties,an algorithm with polynomial time complexity was presented to determine whether a non-primitive BCH code over finite field contains its dual code,which can also be applied to nonnarrow sense primitive BCH codes.
出处
《电子学报》
EI
CAS
CSCD
北大核心
2010年第8期1858-1861,共4页
Acta Electronica Sinica
基金
国家自然科学基金(No.60873101)
江苏省自然科学基金(No.BK2008209)
东南大学优秀博士论文基金(No.YBJJ0820)
关键词
量子纠错码
BCH码
对偶码
循环陪集
quantum error correcting codes
BCH codes
dual codes
cyclotomic cosets
