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A construction of q-ary linear codes with irreducible cyclic codes

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Abstract

Linear codes are an important class of error-correcting codes and widely used in secret sharing schemes, combinational designs, authentication codes and so on. The objective of this paper is to construct q-ary linear codes with good parameters from irreducible cyclic codes. Several classes of linear codes with a few weights including infinite families of distance-optimal ones are derived. The nonzero codewords of some of the codes in this paper have minimal support for inclusion and such codes can be used to construct secret sharing schemes with interesting access structures.

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Acknowledgements

The authors are very grateful to the reviewers and Editors for their detailed comments that much improved the quality and presentation of this paper. This work was supported by the Hong Kong Research Grants Council, Proj. No. 16300415.

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Authors and Affiliations

  1. School of Science, Chang’an University, Xi’an, 710064, China

    Ziling Heng

  2. Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

    Ziling Heng & Cunsheng Ding

Authors
  1. Ziling Heng
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  2. Cunsheng Ding
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Correspondence to Ziling Heng.

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Communicated by V. A. Zinoviev.

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Heng, Z., Ding, C. A construction of q-ary linear codes with irreducible cyclic codes. Des. Codes Cryptogr. 87, 1087–1108 (2019). https://doi.org/10.1007/s10623-018-0507-0

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