JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (06): 59-63.doi: 10.6040/j.issn.1671-9352.0.2014.232

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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

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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

CLC Number: 

  • TN911.22
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