两类厄米特对偶包含的BCH码及其应用  

Two Classes of Hermitian Dual-Containing BCH Codes and Their Applications

作　　者：李锦[1] 高楠 黄山 LI Jin;GAO Nan;HUANG Shan(School of Mathematics,Hefei University of Technology,Hefei,Anhui 230601,China;Anhui Vocational College of Police Officers,Hefei,Anhui 230031,China)

机构地区：[1]合肥工业大学数学学院,安徽合肥230601 [2]安徽警官职业学院,安徽合肥230031

出　　处：《电子学报》2022年第11期2773-2777,共5页Acta Electronica Sinica

基　　金：国家自然科学基金(No.62002093);中央高校基本科研业务费专项资金(No.PA2019GDZC0097)。

摘　　要：Bose-Chaudhuri-Hocquenghem(BCH)码是一类重要的经典纠错码,可以纠正多个错误且具有高效的编码和译码方法,满足一定结构关系的BCH码可以构造量子纠错码.本文研究了有限域上两类BCH码,基于分圆陪集的结构性质,给出了这两类BCH码满足厄米特对偶包含的条件,通过确定每个分圆陪集所含元素个数,计算出了这两类厄米特对偶包含的BCH码的维数,并利用厄米特构造法,由这两类厄米特对偶包含的BCH码得到了一些参数较好的量子纠错码.Bose-Chaudhuri-Hocquenghem(BCH)codes are an important class of classical error-correcting codes,which can correct multiple errors and have efficient coding and decoding methods.BCH codes with certain conditions can be used to construct quantum error-correcting codes.In this paper,we study two classes of BCH codes over finite fields.Based on the structural properties of cyclotomic cosets,we give the conditions for these two classes of BCH codes to be Hermitian dual-containing codes.Then we determine the number of elements contained in each cyclotomic coset,and calculate the dimensions of these two classes of Hermitian dual-containing BCH codes.Furthermore,some quantum error-correcting codes with good parameters are obtained from two classes of Hermitian dual-containing BCH codes by Hermitian construction.

关 键 词：有限域 循环码 BCH码 量子纠错码 厄米特对偶包含码 分圆陪集 

分 类 号：O157.4[理学—数学]