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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (5): 87-92.doi: 10.6040/j.issn.1671-9352.0.2023.247

• • 上一篇    

三阶扭曲广义Reed-Solomon码

张月,闫铭,黄俊松,闫统江*   

  1. 中国石油大学(华东)理学院, 山东 青岛 266580
  • 发布日期:2025-05-19
  • 通讯作者: 闫统江(1973— ),男,教授,博士生导师,博士,研究方向为代数编码学. E-mail:yantoji@163.com
  • 作者简介:张月(1998— ),女,硕士研究生,研究方向为代数编码学. E-mail:zy1159261554zy@163.com*通信作者:闫统江(1973— ),男,教授,博士生导师,博士,研究方向为代数编码学. E-mail:yantoji@163.com
  • 基金资助:
    中央高校基本科研业务费专项资金资助(23CX03003A);山东省自然科学基金资助项目(ZR2022MA061;ZR2023LLZ013)

Twisted generalized Reed-Solomon codes of order three

ZHANG Yue, YAN Ming, HUANG Junsong, YAN Tongjiang *   

  1. College of Science, China University of Petroleum(East China), Qingdao 266580, Shandong, China
  • Published:2025-05-19

摘要: 构造三阶扭曲广义里德-所罗门(twisted generalized Reed-Solomon, TGRS)码,刻画了这类码是极大距离可分(maximum distance separable, MDS)码的充要条件,给出MDS码的新型构造方法,拓展了一阶和二阶MDS-TGRS码的研究。

关键词: 纠错编码, MDS码, 扭曲广义Reed-Solomon码, 广义Reed-Solomon码, Reed-Solomon码

Abstract: Twisted generalized Reed-Solomon(TGRS)codes of order three are constructed. The necessary and sufficient conditions characterizing this class of codes as maximum distance separable(MDS)codes are established. A new construction method for MDS codes is provided and the research on MDS-TGRS codes of order one and order two are expanded.

Key words: error correction coding, MDS codes, twisted generalized Reed-Solomon codes, generalized Reed-Solomon codes, Reed-Solomon codes

中图分类号: 

  • O236.2
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