基于二次乘法特征的射影线性码

陈辅灵; 衡子灵; 王鑫然; 李成举

doi:10.12263/DZXB.20211633

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基于二次乘法特征的射影线性码

学术论文 | 更新时间：2025-07-02

- 基于二次乘法特征的射影线性码
- Projective Linear Codes Based on the Quadratic Multiplicative Characters
- 电子学报 2023年51卷第1期页码：32-41
- 作者机构：
  
  1.长安大学理学院,陕西西安 710064
  2.东南大学移动通信国家重点实验室,江苏南京 210096
  3.华东师范大学高可信计算重点实验室,上海 200062
- 作者简介：
  
  [ "陈辅灵　女，996年9月出生于青海省西宁市.现为长安大学理学院硕士研究生.主要研究方向为代数编码. E-mail: chenfuling1109@163.com" ]
  [ "衡子灵（通讯作者）　男，1990年出生，河南南阳人.现为长安大学理学院副教授，硕士生导师.主要研究方向为编码与密码、序列设计等.E-mail: zilingheng@chd.edu.cn" ]
  [ "王鑫然　男，1999年2月出生于山东省聊城市.现为长安大学理学院硕士研究生.主要研究方向为代数编码. E-mail: WXR782751966@163.com" ]
  [ "李成举　男，1988年6月出生，山东鱼台人.现为华东师范大学教授，博士生导师.主要研究方向为代数编码和信息安全.E-mail: cjli@sei.ecnu.edu.cn" ]
- 基金信息：
  
  国家自然科学基金(11901049;12071138);陕西省高校科协青年人才托举计划(20200505);东南大学移动通信国家重点实验室开放研究基金(2022D05);长安大学中央高校基本科研业务费专项资金(300102122202);上海市可信工业互联网软件协同创新中心项目
- DOI：10.12263/DZXB.20211633
  中图分类号： O236.2
- 收稿：2021-12-08，
  
  修回：2022-05-15，
  
  纸质出版：2023-01-25
- 稿件说明：
移动端阅览
陈辅灵,衡子灵,王鑫然等.基于二次乘法特征的射影线性码[J].电子学报,2023,51(01):32-41.

CHEN Fu-ling,HENG Zi-ling,WANG Xin-ran,et al.Projective Linear Codes Based on the Quadratic Multiplicative Characters[J].ACTA ELECTRONICA SINICA,2023,51(01):32-41.
陈辅灵,衡子灵,王鑫然等.基于二次乘法特征的射影线性码[J].电子学报,2023,51(01):32-41. DOI： 10.12263/DZXB.20211633.

CHEN Fu-ling,HENG Zi-ling,WANG Xin-ran,et al.Projective Linear Codes Based on the Quadratic Multiplicative Characters[J].ACTA ELECTRONICA SINICA,2023,51(01):32-41. DOI： 10.12263/DZXB.20211633.

摘要

基于有限域上的二次乘法特征构造了两类线性码，精确计算出了它们的参数和重量分布.结果表明，第一类线性码是射影三重码，且对偶码关于球填充界几乎最优；第二类线性码是射影二重码，且对偶码关于球填充界几乎最优.此外，本文还得到了一些自正交码和极小码，它们可分别用于构造量子码和安全高效访问结构上的密钥共享方案.

Abstract

Two families of linear codes are constructed based on the quadratic multiplicative characters of finite fields. The parameters and weight distributions of the codes are explicitly determined. It turns out that the first family of linear codes are projective three-weight ones whose duals are almost optimal according to the sphere-packing bound. The second family of linear codes are projective two-weight ones whose duals are also almost optimal according to the sphere-packing bound. Besides

some self-orthogonal codes and minimal codes are obtained. The self-orthogonal codes can be used to construct quantum codes and minimal codes can be used to construct secret sharing schemes with safe and sufficient access structures.

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references

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