ZHU Shixin, HUANG Shan, LI Jin. On the Depth Distribution of Constacyclic Codes over Z4 of Length 2e[J]. Chinese Journal of Electronics, 2019, 28(3): 462-469. doi: 10.1049/cje.2019.03.007
Citation: ZHU Shixin, HUANG Shan, LI Jin. On the Depth Distribution of Constacyclic Codes over Z4 of Length 2e[J]. Chinese Journal of Electronics, 2019, 28(3): 462-469. doi: 10.1049/cje.2019.03.007

On the Depth Distribution of Constacyclic Codes over Z4 of Length 2e

doi: 10.1049/cje.2019.03.007
Funds:  This work is supported by the National Natural Science Foundation of China (No.61772168, No.61572168, No.11501156) and the Natural Science Foundation of Anhui Province (No.1508085SQA198, No.1708085QAO1).
  • Received Date: 2017-01-22
  • Publish Date: 2019-05-10
  • In this paper, we consider the depth distribution of constacyclic codes over Z4 with length even prime power. The depth distribution of negacyclic codes over Z4 of length 2e is completely determined. Furthermore, we determine the depth spectrum of cycilc codes over Z4 of length 2e, and the depth distribution of some cyclic codes over Z4 of length 2e is also given.
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  • R.B. Yehuda, T. Etzion and S. Moran, "Rotating-table games and derivatives of words", Theoretical computer science, Vol.108, No.2, pp.311-329, 1993.
    T. Etzion, "The depth distribution a new characterization for linear codes", IEEE Trans. Inform. Theory, Vol.43, No.4, pp.1361-1363, 1997.
    C.J. Mitchell, "On integer-valued rational polynomials and depth distributions of binary codes", IEEE Trans. Inform. Theory, Vol.44, No.7, pp.3146-3150, 1998.
    Y. Luo, F. Fu and V.W. Wei, "On the depth distribution of linear codes", IEEE Trans. Inform. Theory, Vol.46, No.6, pp.2197-2203, 2000.
    S. Zhu, S. Yang and H. Tong, "On the depth spectrums of linear cyclic codes on ring Z4", Journal of Electronics and Information Technology, Vol.27, No.10, pp.1597-1599, 2005.
    B. Kong, X. Zheng and H. Ma, "The depth spectrums of constacyclic codes over finite chain rings", Discrete Mathematics, Vol.338, No.2, pp.256-261, 2015.
    X. Kai, L. Wang and S. Zhu, "The depth spectrum of negacyclic codes over Z4", Discrete Mathematics, Vol.340, No.3, pp.345-350, 2017.
    J. Wolfmann, "Negacyclic and cyclic codes over Z4", IEEE Trans. Inform. Theory, Vol.45, No.7, pp.2527-2532, 1999.
    T. Blackford, "Negacyclic codes over Z4 of even length", IEEE Trans. Inform. Theory, Vol.49, No.6, pp. 1417-1424, 2003.
    T. Abualrub and R. Oehmke, "On the generators of Z4 cyclic codes of length 2e", IEEE Trans. Inform. Theory, Vol.49, No.9, pp.2126-2133, 2003.
    X. Kai and S. Zhu, "On the distances of cyclic codes of length 2e over Z4", Discrete Mathematics, Vol.310, No.1, pp.12-20, 2010.
    H.Q. Dinh, "Complete distances of all negacyclic codes of length 2s over Z2a", IEEE Trans. Inform. Theory, Vol.53, No.1, pp.147-161, 2007.
    T. Blackford, "Cyclic codes over Z4 of oddly even length", Discrete Applied Mathematics, Vol.128, No.1, pp.27-46, 2003.
    A. Sălăgean, "Repeated-root cyclic and negacyclic codes over a finite chain ring", Discrete applied mathematics, Vol.154, No.2, pp.413-419, 2006.
    S.T. Dougherty and S. Ling, "Cyclic codes over Z4 of even length", Designs Codes and Cryptography, Vol.39, No.2, pp.127-153, 2006.
    H.Q. Dinh and S.R. López-Permouth, "Cyclic and negacyclic codes over finite chain rings", IEEE Trans. Inform. Theory, Vol.50, No.8, pp.1728-1744, 2004.
    M. Shi, "Optimal p-ary codes from one-weight linear codes over Z pm", Chinese Journal of Electronics, Vol.22, No.4, pp.799-802, 2013.
    M. Shi, "Optimal p-ary codes from constacyclic codes over a non-chain ring R", Chinese Journal of Electronics, Vol.23, No.4, pp.773-777, 2014.
    M. Shi, T. Yao and P. Solé, "Skew cyclic codes over a nonchain ring", Chinese Journal of Electronics, Vol.26, No.3, pp.544-547, 2017.
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