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)
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  • 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.
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