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Several classes of linear codes and their weight distributions

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

In this paper, several classes of two-weight or three-weight linear codes over \( {{\mathbb {F}}}_p\) from quadratic or non-quadratic functions are constructed and their weight distributions are determined. From the constructed codes, we obtain some optimal linear codes with respect to the Singleton bound and the Griesmer bound. These two- or three-weight linear codes may have applications in secret sharing, authentication codes, association schemes and strongly regular graphs.

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Acknowledgements

The authors would like to thank Prof. Q. Xiang for providing Reference [13], and the reviewers and the editor for their helpful comments and valuable suggestions, which have greatly improved the presentation of this paper. This work of X. Wang and H. Liu was supported by the self-determined research funds of CCNU from the collegess basic research and operation of MOE (Grant No. CCNU18TS028).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Xiaoqiang Wang & Hongwei Liu

  2. Hubei Province Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

    Dabin Zheng

Authors
  1. Xiaoqiang Wang
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  2. Dabin Zheng
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  3. Hongwei Liu
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Correspondence to Dabin Zheng.

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Wang, X., Zheng, D. & Liu, H. Several classes of linear codes and their weight distributions. AAECC 30, 75–92 (2019). https://doi.org/10.1007/s00200-018-0359-x

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  • DOI: https://doi.org/10.1007/s00200-018-0359-x

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