YAO Ting, ZHU Shixin, KAI Xiaoshan. Asymptotically Good Additive Cyclic Codes[J]. Chinese Journal of Electronics, 2020, 29(5): 859-864. doi: 10.1049/cje.2020.05.013
Citation: YAO Ting, ZHU Shixin, KAI Xiaoshan. Asymptotically Good Additive Cyclic Codes[J]. Chinese Journal of Electronics, 2020, 29(5): 859-864. doi: 10.1049/cje.2020.05.013

Asymptotically Good Additive Cyclic Codes

doi: 10.1049/cje.2020.05.013
Funds:  This work is supported by the National Natural Science Foundation of China (No.61772168, No.61972126)
More Information
  • Corresponding author: ZHU Shixin (corresponding author) was born in 1962. He is a professor and Ph.D. supervisor of Hefei University of Technology. His research interests include algebra coding theory, information security and sequence cipher. (Email:zhushixinmath@hfut.edu.cn)
  • Received Date: 2019-11-05
  • Rev Recd Date: 2020-01-18
  • Publish Date: 2020-09-10
  • ZpZps-additive cyclic codes have been proved to be asymptotically good by Yao and Zhu. For binary Hamming scheme, we introduce a type of Z2(Z2 + uZ2)-additive cyclic codes generated by pairs of polynomials. Let R be the chain ring Z2 + uZ2, where u2=0. The asymptotic rates and relative distances of this class of codes are presented by establishing the relationship between the random Z2R-additive cyclic code and random binary quasi-cyclic code of index 2. We show that Z2R-additive cyclic codes are asymptotically good.
  • loading
  • R. R. Varshamov, "Estimate of the number of signals in error correcting codes", Dokl. Akad. Nauk SSSR, Vol.117, No.5, pp.739-741, 1957.
    L. M. J. Bazzi and S. K. Mitter, "Some randomized code constructions from group actions", IEEE Trans. Inform. Theory, Vol.52, No.7, pp.3210-3219, 2006.
    C. L. Chen, W. W. Peterson and E. J. Weldon, "Some results on quasi-cyclic codes", Inf. Control., Vol.15, No.5, pp.407-423, 1969.
    V. V. Chepyzhov, "New lower bounds for minimum distance of linear quasi-cyclic and almost linear cyclic codes", Problemy Peredachi Inform., Vol.28, No.1, pp.39-51, 1992.
    C. Martinez-Perez and W. Willems, "Is the class of cyclic codes asymptotically good?", IEEE Trans. Inform. Theory, Vol.52, No. 2, pp.696-700, 2006.
    A. Alahmadi, C. Güneri, H. Shoaib, et al., "Long quasipolycyclic t-CIS codes", Adv. Math Commun., Vol.2, No.1, pp.189-198, 2018.
    M. J. Shi, R. S. Wu and P. Solé, "Asymptotically good additive cyclic codes exist", IEEE Communications Letters, Vol.22, No.10, pp.1980-1983, 2018.
    M.J. Shi, D.T. Huang, L. Sok, et al., "Double circulant LCD codes over Z4", Finite Fields and Their Applications, Vol.58, pp.133-144, 2019.
    M. J. Shi, L. Q. Qian and P. Solé, "On self-dual negacirculant codes of index two and four", Designs, Codes and Cryptography, Vol.86, pp. 2485-2494, 2018.
    S. Ling and P. Solé, "Good self-dual quasi-cyclic codes exist", IEEE Trans. Inform. Theory, Vol.49, No.4, pp.1052-1053, 2003.
    M. J. Shi, L. Q. Qian, Y. Liu, et al., " Good self-dual generalized quasi-cyclic codes exist", Information Processing Letters, Vol.118, pp.21-24, 2017.
    T. Yao and S. X. Zhu, "ZpZps-additive cyclic codes are asymptotically good", Cryptography and Communications, DOI:10.1007/s12095-019-00397-z, 2019.
    P. Delsarte, "An Algebraic Approach to Association Schemes of Coding Theory", ser. Philips Res. Rep., Supplement, 1973.
    T. Abualrub, I. Siap and H. Aydin, "Z2Z4", IEEE Transactions on Information Theory, Vol.60, No.3, pp.1508-1514, 2014.
    B. Srinivasulu and M. Bhaintwal, "Z2(Z2+ uZ2)-Additive cyclic codes and their duals', Discrete Mathematics Algorithms and Applications, Vol.8, No.2, DOI:10.1142/S1793830916500270, 2016.
    M.J. Shi, L. Q. Qian, L. Sok, et al., "On constacyclic codes over Z4[u]/2-1> and their Gray images", Finite Fields and Their Applications, Vol.45, pp.86-95, 2017.
    Database of Z4 codes, http://www.z4codes.info,2016-9-3.
    H.L. Liu, "Three questions about quasi-cyclic codes and constacyclic codes", Ph.D. Thesis, Central China Normal University, Wuhan, China, 2018. (in Chinese)
    I. Aydogdu, T. Abualrub and I. Siap, "On Z2Z2[u]-additive codes", Int. J. Comput. Math., Vol.92, No.9, pp.1806-1814, 2015.
    Y. Fan and H. L. Liu, "Double circulant matrices", Linear and Multil. Algebra, Vol.66, No. 10, pp.2119-2137, 2018.
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (125) PDF downloads(63) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint