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

Previous Articles     Next Articles

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

PDF (PC)

667

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
[1] DE BOER M A. Almost MDS codes[J]. Designs, Codes and Cryptogr, 1996, 9:143-155.
[2] DODUNEKOV S, LANDJEV I N. On near-MDS codes[J]. J Geom, 1995, 59:43-51.
[3] 朱雪秀,刘九分,张卫明. 一种基于汉明码和湿纸码的隐写算法[J].电子与信息学报, 2010,32(1):162-165. ZHU Xuexiu, LIU Jiufen, ZHANG Weiming. A steganographic algorithm based on Hamming code and wet paper code[J]. Journal of Electronics and Information Technology, 2010, 32(1):162-165.
[4] 刘九分, 李玉辉, 陈嘉勇,等. 基于三元Golay隐写码的快速隐写算法[J]. 计算机工程,2008,34(24):149-151. LIU Jiufen, LI Yuhui, CHEN Jiayong, et al. Fast steganographic algorithm based on ternary steganographic Golay code[J]. Computer Engineering, 2008, 34(24):149-151.
[5] WORD J. Duality for modules over finite rings and applications to coding theory[J]. Amer J Math, 1999, 121:555-575.
[6] HUFFMAN W C, PLESS V S. Fundamentals of error-correcting codes[M]. Cambridge: Cambridge University Press, 2003.
[7] DOUGHERT S T, KIM J L, KULOSMAN H. MDS codes over finite principal ideal rings[J]. Designs, Codes and Cryptogr, 2009, 50(1):77-92.
[8] DOUGHERT S T, LIU Hongwei. Independence of vectors in codes over rings[J].Designs, Codes and Cryptogr, 2009, 51(1):58-68.
[9] CONWAY H, SLOANE N J A. Self-dual codes over the integers modulo 4[J]. J Combin Theorey: Ser A, 1993, 62:30-45.
[10] DOUGHERT S T, PARK Y H, KIM S Y. Lifted codes and their weight enumerators[J]. Discrete Mathematics, 2005, 305(1-3):123-135.
[11] NORTON G H, SALAGEAN A. On the structure of linear and cyclic codes over finite chain ring[J]. Applicable Algebra in Engineering, Communication and Computing, 2000, 10:489-506.
[12] 邢朝平, 冯克勤. 线性码的重量分布[J].数学的实践与认识, 1990, 2:20-23. XING Chaoping, FENG Keqin. Weight distribution of linear codes[J]. Mathematics in Practice and Theory, 1990, 2:20-23.
[13] NORTON G H, SALAGEAN A. On the Hamming distance of linear codes over a finite chain ring[J]. IEEE Trans Inform Theory, 2000, 46(2):1060-1067.
[1] LIU Cai-ran, SONG Xian-mei. Quadratic residue codes over Fl+vFl+v2Fl [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 45-49.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd