Abstract
In this paper, we investigate all coset leaders of primitive BCH codes for \(\delta\) in the range \(1\le \delta \le q^\frac{m+7}{2}\), which extends Liu and Shi’s results. Besides, we also generalize Shi’s results by proposing the maximum designed distance of non-narrow-sense(\(b=k_2q^2+k_1q+k_0\)) primitive BCH codes which can contain their Euclidean dual. At the end, we calculate the dimension of the Euclidean dual containing non-narrow-sense primitive BCH codes and construct some quantum BCH codes.
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (No. 61772015), the Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-17-010) and the Foundation of Jinling Institute of Technology (No. JIT-B-202016). The authors are very thankful to the reviewers and the editor for their valuable comments and suggestions to this paper.
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Huang, X., Yue, Q., Shi, X. et al. Quantum BCH codes with maximum designed distance. AAECC 33, 213–236 (2022). https://doi.org/10.1007/s00200-020-00443-x
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DOI: https://doi.org/10.1007/s00200-020-00443-x