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Designed distances and parameters of new LCD BCH codes over finite fields

  • Fengwei LiEmail author
  • Qin Yue
  • Yansheng Wu
Article
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Abstract

Let \(\mathbb {F}_{q}\) be the finite field of q elements and n = qm − 1 with m a positive integer. In this paper we construct a class of BCH and LCD BCH codes of length n over \(\mathbb {F}_{q}\) and investigate their dimensions and designed distance. Our results show that the designed distances of BCH and LCD BCH codes in this paper are larger than those in [11, Theorems 7, 10, 18, and 22]. It is viewed as a generalized result of [11].

Keywords

BCH code Cyclic code Linear code LCD code 

Mathematics Subject Classification (2010)

94B15 11T71 11T24 

Notes

Acknowledgments

The paper was supported by National Natural Science Foundation of China under Grants 11601475, 61772015 and Foundation of Science and Technology on Information Assurance Labo- ratory under Grant KJ-17-010.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZaozhuang UniversityZaozhuangPeople’s Republic of China
  2. 2.State Key Laboratory of CryptologyBeijingPeople’s Republic of China
  3. 3.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China

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