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MacWilliams identities of linear codes with respect to RT metric over Mn×s(F l+v F l+…+vk-1 l)

  • School of Mathematical Sciences, Anhui University, Hefei 230601, China

Funds:  Supported by National Natural Science Foundation of China (61672036), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China (05015133), the Open Research Fund of National Mobile Communications Research Laboratory, Southeast University (2015D11), Key Projects of Support Program for Outstanding Young Talents in Colleges and Universities (gxyqZD2016008).
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2018.02.002
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  • Author Bio:

    WU Rongsheng, male, born in 1992, master. Research field: Algebraic coding. E-mail: wrs2510@163.com

  • Corresponding author: SHI Minjia
  • Received Date: 10 January 2017
  • Rev Recd Date: 13 December 2017
  • Publish Date: 28 February 2018
    Abstract

  • Abstract

    A new Gray map over the commutative ring R=

    Abstract

    A new Gray map over the commutative ring R=
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    • References(11)
  • [1]
    ROSENBLOOM M Y, TSFASMAN M A. Codes for the m-metric[J]. Problems of Information Transmission, 1997, 33(33): 55-63.
    [2]
    DU W, XU H Q. MacWilliams identities of linear codes over ring Mn×s(R) with respect to the Rosenbloom-Tsfasman metric[J]. Information Technology Journal, 2012, 11(12): 1770-1775.
    [3]
    WANG D D, SHI M J, LIU Y. MacWilliams identities of linear codes over a matrix ring with respect to Rosenbloom-Tsfasman metric[J]. International Journal of Information and Electronics Engineering, 2015, 5(3): 184-188.
    [4]
    AMIT K S, ANURADHA S. MacWilliams identities for weight enumerators with respect to the RT metric[J]. Discrete Mathematics Algorithms and Applications, 2014, 6(2): 1450030.
    [5]
    SIAP I. A MacWilliams type identity[J]. Turkish Journal of Mathematics, 2002, 26(4): 181-194.
    [6]
    SIAP I. The complete weight enumerator for codes over Mn×s(Fq)[J]. Lecture Notes on Computer Sciences, 2001, 2260(1): 20-26.
    [7]
    SIAP I, OZEN M. The complete weight enumerator for codes over Mn×s(R)[J]. Applied Mathematics Letters, 2004, 17(1): 65-69.
    [8]
    SHI M J, LIU Y, SOL P. MacWilliams identities of linear codes with respect to RT metric over Mn×s(Fl + vFl + v2Fl)[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2014, E97-A(8): 1810-1813.
    [9]
    SHI M J, SOL P, WU B. Cyclic codes and the weight enumerator of linear codes over F2 +vF2 +v2F2[J]. Applied and Computational Mathematics, 2013, 12(2): 247-255.
    [10]
    MACWILLIAMS F J, SLOANE N J A. The Theory of Error Correcting Codes[M]. Amsterdam: North-Holland Publishing Co, 1997.
    [11]
    ZHU S X, XU H Q, SHI M J. MacWilliams identity with respect to RT metric over ring Z4[J]. Acta Electronica Sinica, 2009, 37: 1116-1118.
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    [1]
    ROSENBLOOM M Y, TSFASMAN M A. Codes for the m-metric[J]. Problems of Information Transmission, 1997, 33(33): 55-63.
    [2]
    DU W, XU H Q. MacWilliams identities of linear codes over ring Mn×s(R) with respect to the Rosenbloom-Tsfasman metric[J]. Information Technology Journal, 2012, 11(12): 1770-1775.
    [3]
    WANG D D, SHI M J, LIU Y. MacWilliams identities of linear codes over a matrix ring with respect to Rosenbloom-Tsfasman metric[J]. International Journal of Information and Electronics Engineering, 2015, 5(3): 184-188.
    [4]
    AMIT K S, ANURADHA S. MacWilliams identities for weight enumerators with respect to the RT metric[J]. Discrete Mathematics Algorithms and Applications, 2014, 6(2): 1450030.
    [5]
    SIAP I. A MacWilliams type identity[J]. Turkish Journal of Mathematics, 2002, 26(4): 181-194.
    [6]
    SIAP I. The complete weight enumerator for codes over Mn×s(Fq)[J]. Lecture Notes on Computer Sciences, 2001, 2260(1): 20-26.
    [7]
    SIAP I, OZEN M. The complete weight enumerator for codes over Mn×s(R)[J]. Applied Mathematics Letters, 2004, 17(1): 65-69.
    [8]
    SHI M J, LIU Y, SOL P. MacWilliams identities of linear codes with respect to RT metric over Mn×s(Fl + vFl + v2Fl)[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2014, E97-A(8): 1810-1813.
    [9]
    SHI M J, SOL P, WU B. Cyclic codes and the weight enumerator of linear codes over F2 +vF2 +v2F2[J]. Applied and Computational Mathematics, 2013, 12(2): 247-255.
    [10]
    MACWILLIAMS F J, SLOANE N J A. The Theory of Error Correcting Codes[M]. Amsterdam: North-Holland Publishing Co, 1997.
    [11]
    ZHU S X, XU H Q, SHI M J. MacWilliams identity with respect to RT metric over ring Z4[J]. Acta Electronica Sinica, 2009, 37: 1116-1118.
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