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A class of new group character codes and convolutional codes

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Abstract

In this paper, we construct a class of new group character codes with parameters \([2^n,2^n-2S_n(r-1),2^r]\) based on Ding et al. (IEEE Trans Inf Theory 46(1):280–284, 2000). Moreover, we use the new group character codes to construct a family of unit memory convolutional codes with parameters \([2^n,2^n-S_n(r-1),S_n(r-1);1,2^r]\), which the free distances of these convolutional codes are exact values.

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Acknowledgements

The authors would like to sincerely thank the anonymous referees and the Editor for their valuable comments and suggestions, which help to improve the quality of this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, People’s Republic of China

    Fengwei Li

  2. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, People’s Republic of China

    Fengwei Li & Qin Yue

  3. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, People’s Republic of China

    Fengwei Li & Qin Yue

  4. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, People’s Republic of China

    Qin Yue

Authors
  1. Fengwei Li
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  2. Qin Yue
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Correspondence to Fengwei Li.

Additional information

The paper is supported by National Natural Science Foundation of China (No. 11601475) and Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-15-009).

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Li, F., Yue, Q. A class of new group character codes and convolutional codes. J. Appl. Math. Comput. 57, 577–589 (2018). https://doi.org/10.1007/s12190-017-1122-3

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  • DOI: https://doi.org/10.1007/s12190-017-1122-3

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