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山东大学学报(理学版) ›› 2015, Vol. 50 ›› Issue (06): 59-63.doi: 10.6040/j.issn.1671-9352.0.2014.232

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有限主理想环上接近MDR码

张晓燕   

  1. 湖北理工学院数理学院, 湖北 黄石 435003
  • 收稿日期:2014-05-23 修回日期:2014-11-05 出版日期:2015-06-20 发布日期:2015-07-31
  • 作者简介:张晓燕,(1979-),女,硕土,副教授,研究方向为代数编码.E-mail:zhangxiaoyan300@126.com
  • 基金资助:
    湖北省教育厅自然科学基金重点项目(D20144401)

Near-MDR codes over finite principal ideal rings

ZHANG Xiao-yan   

  1. School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, Hubei, China
  • Received:2014-05-23 Revised:2014-11-05 Online:2015-06-20 Published:2015-07-31

摘要: 将有限域上接近MDS码的概念推广到有限主理想环上的接近MDR码。利用有限主理想环上线性码为有限链环上线性码的中国积,将有限主理想环上线性码为接近MDR码的判定转化成有限链环上接近MDR码的判定。进一步,将有限链环上接近MDR码的判定转化为它的剩余类域上接近MDS码的判定,从而描述了有限主理想环上接近MDR码。

关键词: 有限主理想环, 几乎MDR码, 接近MDR码, 有限链环

Abstract: The definition of Near-MDS codes over finite fields was generalized to near-MDR codes over finite principal ideal rings. Using the fact that a linear codes over a finite principal ideal ring is the Chinese product of the linear codes over finite chain rings, the criterion of near-MDR codes over finite principal ideal rings are changed into that of near-MDR codes over finite chain rings. Furthermore, the criterion of near-MDR codes over finite chain rings is changed into that of near-MDS codes over residue fields, so we describe near-MDR codes over finite principal ideal rings.

Key words: almost MDR codes, near-MDR codes, finite principal rings, finite chain rings

中图分类号: 

  • TN911.22
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