电子学报 ›› 2022, Vol. 50 ›› Issue (11): 2773-2777.DOI: 10.12263/DZXB.20210951

• 学术论文 • 上一篇    下一篇

两类厄米特对偶包含的BCH码及其应用

李锦1, 高楠1, 黄山2   

  1. 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
  • 收稿日期:2021-07-20 修回日期:2021-11-12 出版日期:2022-11-25
    • 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
    • 基金资助:
    • 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)

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

LI Jin1, GAO Nan1, HUANG Shan2   

  1. 1.School of Mathematics,Hefei University of Technology,Hefei,Anhui 230601,China
    2.Anhui Vocational College of Police Officers,Hefei,Anhui 230031,China
  • Received:2021-07-20 Revised:2021-11-12 Online:2022-11-25 Published:2022-11-19

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.

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

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.

Key words: finite fields, cyclic codes, BCH codes, quantum error-correcting codes, Hermitian dual-containing codes, cyclotomic cosets

中图分类号: