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Skew cyclic codes over F q[u,v]/〈u2-1, v3-v, uv-vu〉

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

Funds:  Supported by NNSF 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) and Key projects of support program for outstanding young talents in Colleges and Universities (gxyqZD2016008), Natural Science Research Project of Higher Education of Anhui Province of China(KJ2015JD18).
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2017.10.009
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  • Author Bio:

    GUAN Yue, female, born in 1994, Master candidate. Research field: algebra code. E-mail: guanyueeee@163.com

  • Corresponding author: SHI Minjia
  • Received Date: 09 June 2016
  • Rev Recd Date: 07 January 2017
  • Publish Date: 31 October 2017
    Abstract

  • Abstract

    The skew cyclic codes over R=

    Abstract

    The skew cyclic codes over R=
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    • References(13)
  • [1]
    BOUCHER D, GEISELMANN W, ULMER F. Skew-cyclic codes[J]. Applicable Algebra Engineering Communication & Computing, 2007, 18(4) 379-389.
    [2]
    BOUCHER D, ULMER F. Coding with skew polynomial ring[J]. Journal of Symbolic Computation, 2009, 44(12): 1644-1656.
    [3]
    CAO Y L. Quasi-cyclic codes of index 2 and skew polynomial rings over finite fields[J]. Finite Fieids and Their Applications, 2014, 27: 143-158.
    [4]
    BOUCHER D, ULMER F. Self-dual skew codes and factorization of skew polynomials[J]. Journal of Symbolic Computation, 2014, 60(1): 47-61.
    [5]
    ABUALRUB T, GHRAYEB A, AYDIN N, et al. On the construction of skew quasi-cyclic codes[J]. IEEE Transactions on Information Theory, 2010, 56(5): 2081-2090.
    [6]
    JITMAN S, LING S, UDOMKAVANICH P. Skew constacyclic codes over finite chain rings[J]. Advances in Mathematics Communications, 2010, 6(1): 39-63.
    [7]
    AYDIN N, ABUALRUB T, SENEVIRATNE P. On θ-cyclic codes over F2+vF2[J]. Australian Journal of Combinatorics, 2012, 54: 115-126.
    [8]
    GAO J. Skew cyclic codes over Fp + vFp[J]. Journal of applied mathematics & informatics, 2013, 31(3-4): 337-342.
    [9]
    GURSOY F, SIAP I, YILDIZ B. Construction of skew cyclic codes over Fq+vFq[J]. Advances in Mathematics of Communications, 2014, 8(3): 313-322.
    [10]
    ASHRAF M, GHULAM M. On skew cyclic codes over F3 + vF3[J]. International Journal of Information & Coding Theory, 2014, 2(4): 218-225.
    [11]
    SHI M J, YAO T, ALAHMADI A, et al. Skew cyclic codes over Fp+vFp+v2Fq[J]. The Institute of Electronics, Information and Communication Engineers, 2015, 98(8): 1845-1848.
    [12]
    YAO T, SHI M J, SOL P. Skew cyclic codes over Fp +u Fp +vFq +uvFq[J]. Journal of Algebra Combinatorics Discrete Structures & Applications, 2015, 2(3): 163-168.
    [13]
    SIAP I, ABUALRUB T, AYDIN N, et al. Skew cyclic codes of arbitrary length[J]. International Journal of Information & Coding Theory, 2011, 2(1): 10-20.
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    [1]
    BOUCHER D, GEISELMANN W, ULMER F. Skew-cyclic codes[J]. Applicable Algebra Engineering Communication & Computing, 2007, 18(4) 379-389.
    [2]
    BOUCHER D, ULMER F. Coding with skew polynomial ring[J]. Journal of Symbolic Computation, 2009, 44(12): 1644-1656.
    [3]
    CAO Y L. Quasi-cyclic codes of index 2 and skew polynomial rings over finite fields[J]. Finite Fieids and Their Applications, 2014, 27: 143-158.
    [4]
    BOUCHER D, ULMER F. Self-dual skew codes and factorization of skew polynomials[J]. Journal of Symbolic Computation, 2014, 60(1): 47-61.
    [5]
    ABUALRUB T, GHRAYEB A, AYDIN N, et al. On the construction of skew quasi-cyclic codes[J]. IEEE Transactions on Information Theory, 2010, 56(5): 2081-2090.
    [6]
    JITMAN S, LING S, UDOMKAVANICH P. Skew constacyclic codes over finite chain rings[J]. Advances in Mathematics Communications, 2010, 6(1): 39-63.
    [7]
    AYDIN N, ABUALRUB T, SENEVIRATNE P. On θ-cyclic codes over F2+vF2[J]. Australian Journal of Combinatorics, 2012, 54: 115-126.
    [8]
    GAO J. Skew cyclic codes over Fp + vFp[J]. Journal of applied mathematics & informatics, 2013, 31(3-4): 337-342.
    [9]
    GURSOY F, SIAP I, YILDIZ B. Construction of skew cyclic codes over Fq+vFq[J]. Advances in Mathematics of Communications, 2014, 8(3): 313-322.
    [10]
    ASHRAF M, GHULAM M. On skew cyclic codes over F3 + vF3[J]. International Journal of Information & Coding Theory, 2014, 2(4): 218-225.
    [11]
    SHI M J, YAO T, ALAHMADI A, et al. Skew cyclic codes over Fp+vFp+v2Fq[J]. The Institute of Electronics, Information and Communication Engineers, 2015, 98(8): 1845-1848.
    [12]
    YAO T, SHI M J, SOL P. Skew cyclic codes over Fp +u Fp +vFq +uvFq[J]. Journal of Algebra Combinatorics Discrete Structures & Applications, 2015, 2(3): 163-168.
    [13]
    SIAP I, ABUALRUB T, AYDIN N, et al. Skew cyclic codes of arbitrary length[J]. International Journal of Information & Coding Theory, 2011, 2(1): 10-20.
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