Dual-Containing Determination Method for Non-Primitive BCH Codes over Finite Field

XIAO Fang-ying; CHEN Han-wu; LIU Zhi-hao; LI Zhi-qiang; LIU Wen-jie

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Dual-Containing Determination Method for Non-Primitive BCH Codes over Finite Field

更新时间：2025-07-16

- Dual-Containing Determination Method for Non-Primitive BCH Codes over Finite Field
- Acta Electronica Sinica Vol. 38, Issue 8, Pages: 1858-1861(2010)
- 作者机构：
  
  1. 东南大学计算机科学与工程学院,江苏,南京,210096
  2. 扬州大学信息工程学院计算机科学与技术系,江苏,扬州,225009
  3. 南京信息工程大学计算机科学与软件学院,江苏,南京,210044
  4. 东南大学计算机科学与工程学院江苏南京,210096
  5. 扬州大学信息工程学院计算机科学与技术系,江苏,扬州,225009
  6. 南京信息工程大学计算机科学与软件学院江苏南京,210044
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP387
- Published：2010
- 稿件说明：
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XIAO Fang-ying, CHEN Han-wu, LIU Zhi-hao, et al. Dual-Containing Determination Method for Non-Primitive BCH Codes over Finite Field[J]. Acta Electronica Sinica, 2010, 38(8): 1858-1861.
DOI：

XIAO Fang-ying, CHEN Han-wu, LIU Zhi-hao, et al. Dual-Containing Determination Method for Non-Primitive BCH Codes over Finite Field[J]. Acta Electronica Sinica, 2010, 38(8): 1858-1861. DOI：

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.

Abstract

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.

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