两类厄米特对偶包含的BCH码及其应用

李锦; 高楠; 黄山

doi:10.12263/DZXB.20210951

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两类厄米特对偶包含的BCH码及其应用

学术论文 | 更新时间：2025-12-08

- 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
- 电子学报 2022年50卷第11期页码：2773-2777
- 作者机构：
  
  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
- 作者简介：
  
  [ "李锦女，1987年1月出生于陕西省彬州市，现为合肥工业大学数学学院副教授，研究方向为代数编码.E‑mail: lijin_0102@126.com" ]
  [ "高楠女，1997年8月出生于安徽省蚌埠市，现为合肥工业大学数学学院硕士研究生，研究方向为代数编码.E‑mail: gaonan_2775@163.com" ]
  [ "黄山女，1993年5月出生于安徽省桐城市，现为安徽警官职业学院教师，研究方向为代数编码.E‑mail: huangshan5197@163.com" ]
- 基金信息：
  
  国家自然科学基金(62002093);中央高校基本科研业务费专项资金(PA2019GDZC0097)
- DOI：10.12263/DZXB.20210951
  中图分类号： O157.4
- 收稿：2021-07-20，
  
  修回：2021-11-12，
  
  纸质出版：2022-11-25
- 稿件说明：
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李锦,高楠,黄山.两类厄米特对偶包含的BCH码及其应用[J].电子学报,2022,50(11):2773-2777.

LI Jin,GAO Nan,HUANG Shan.Two Classes of Hermitian Dual-Containing BCH Codes and Their Applications[J].ACTA ELECTRONICA SINICA,2022,50(11):2773-2777.
李锦,高楠,黄山.两类厄米特对偶包含的BCH码及其应用[J].电子学报,2022,50(11):2773-2777. DOI： 10.12263/DZXB.20210951.

LI Jin,GAO Nan,HUANG Shan.Two Classes of Hermitian Dual-Containing BCH Codes and Their Applications[J].ACTA ELECTRONICA SINICA,2022,50(11):2773-2777. DOI： 10.12263/DZXB.20210951.

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.

Abstract

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.

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Keywords

references

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