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Complete weight enumerators of some linear codes and their applications

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Abstract

Recently, linear codes constructed from defining sets have been extensively studied. It was shown that the linear codes may have a few nonzero weights or be optimal if the defining sets are well chosen. The weight enumerators of these linear codes were also presented. In this paper, we investigate the complete weight enumerators of some linear codes constructed from the defining sets. As applications, we employ the explicit complete weight enumerators of the linear codes to construct constant composition codes and systematic authentication codes. A new class of optimal constant composition codes and three classes of asymptotically optimal systematic authentication codes are presented.

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Acknowledgments

The authors are very grateful to the editor and the anonymous reviewers for their valuable comments and suggestions that improved the quality of this paper. This paper is supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIP) (ASARC, NRF-2007-0056093), the National Natural Science Foundation of China (Nos. 11171150, 11271381, 11431015, and 61472457), the Fundamental Research Funds for the Central Universities (No. 56XZA15002), the 973 Program of China (Grant No. 2011CB808000), and the Natural Science Foundation of Guangdong (Grant No. 2014A030313161).

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Authors and Affiliations

  1. Department of Mathematics, KAIST, Daejeon, 305-701, Korea

    Chengju Li & Sunghan Bae

  2. Department of Mathematics, Chungnam National University, Daejeon, 305-764, Korea

    Jaehyun Ahn

  3. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China

    Shudi Yang & Zheng-An Yao

  4. School of Mathematical Sciences, Qufu Normal University, Shandong, 273165, People’s Republic of China

    Shudi Yang

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  1. Chengju Li
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  2. Sunghan Bae
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  3. Jaehyun Ahn
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Correspondence to Jaehyun Ahn.

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Communicated by C. Ding.

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Li, C., Bae, S., Ahn, J. et al. Complete weight enumerators of some linear codes and their applications. Des. Codes Cryptogr. 81, 153–168 (2016). https://doi.org/10.1007/s10623-015-0136-9

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