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A kind of three-weight linear codes

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Abstract

Recently, linear codes with few weights have been constructed through defining sets. Results show that some optimal codes can be obtained if the defining sets were well chosen. In this paper, we investigate the linear codes constructed from the absolute trace function. It is shown that the constructed codes are binary linear codes with three weights. The dual codes of the proposed linear codes are also studied and proved to be optimal or almost optimal.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100195, China

    Qiuyan Wang, Kelan Ding, Dongdai Lin & Rui Xue

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Qiuyan Wang & Kelan Ding

Authors
  1. Qiuyan Wang
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  2. Kelan Ding
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  3. Dongdai Lin
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  4. Rui Xue
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Corresponding author

Correspondence to Kelan Ding.

Additional information

This research is supported by a National Key Basic Research Project of China (2011CB302400), National Natural Science Foundation of China (61379139) and the “Strategic Priority Research Program” of the Chinese Academy of Sciences, Grant No. XDA06010701.

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Wang, Q., Ding, K., Lin, D. et al. A kind of three-weight linear codes. Cryptogr. Commun. 9, 315–322 (2017). https://doi.org/10.1007/s12095-015-0180-3

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  • DOI: https://doi.org/10.1007/s12095-015-0180-3

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