几类量子BCH码的构造  

Several Classes of Quantum BCH Codes

作　　者：蒲可莉 廖群英 PU Keli;LIAO Qunying(School of Mathematics and Science,Sichuan Normal University,Chengdu 610066,Sichuan;Institute of Mathematics,Aba Teachers College,Wenchuan 623000,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066 [2]阿坝师范学院数学学院,四川汶川623000

出　　处：《四川师范大学学报（自然科学版）》2024年第5期689-695,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(12071321);四川省科技计划资助项目(23ZYZYTS0335)。

摘　　要：量子纠错码可以有效地克服量子消相干,是实现量子计算的关键技术.量子纠错码可以利用满足特定关系的经典纠错码来进行构造.BCH码作为一类距离可设计的特殊循环码,具有很好的代数结构,所以可以用来构造量子BCH码.首先给出有限域F_(q)(q为素数方幂)上模n分圆陪集是单元集的等价刻画和性质.然后利用CSS构造和Steane构造得到两类有限域F_(q)上的新的量子BCH码,最后将分圆陪集的相关结果推广到有限域F_(q^(2))上,并利用Hermitian构造得到一类量子BCH码.Quantum error-correcting codes can be used to overcome quantum decoherence efficiently,which is the key technology to realize quantum computing.A series of quantum codes were proposed based on classical codes.In this paper,a necessary and sufficient condition for being the number of elements in cyclotomic cosets over finite fields is given and then some characteristics for cyclotomic cosets over finite fields are presented.Later,a series of new quantum BCH codes over the finite field F_(q)are constructed by CSS(Calderbank-Shor-Steane)construction or Steane construction,where q is a power of the prime.Finally,a class of quantum BCH codes over F_(q^(2))are constructed by using Hermitian construction.

关 键 词：分圆陪集 CSS构造 Steane构造 Hermitian构造 量子BCH码 

分 类 号：O236.2[理学—运筹学与控制论]