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BCH codes with larger dimensional hull

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Abstract

Hulls of linear codes are widely studied due to their good properties and wide applications. Let \(n=\frac{q^m-1}{r}\) and \(\mathcal {C}\) be an [n, k] cyclic code over \(\mathbb {F}_q\), where \(r|q-1\). In this paper, we present several necessary and sufficient conditions for BCH codes of length n that have \(k-1\) or \(k^\perp -1\) dimensional hulls, where \(k^\perp \) is the dimension of \(\mathcal {C}^\perp \). Further, we give the parameters of several families of self-orthogonal codes that arise as hulls of BCH codes. We obtain many optimal codes.

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The data that support the findings of this study are available from the corresponding author, Binbin Pang, upon reasonable request.

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Acknowledgements

This research was supported by the Fundamental Research Funds for the Central Universities under Gran JZ2022HGQB021, the National Natural Science Foundation of China under Grant U21A20428 and 12171134. We declare that we have no conflict of interest.

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230009, Anhui, People’s Republic of China

    Binbin Pang & Shixin Zhu

  2. School of Computer and Information, Hefei University of Technology, Hefei, 230009, Anhui, People’s Republic of China

    Tian Yang & Jun Gao

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  1. Binbin Pang
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  2. Shixin Zhu
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  4. Jun Gao
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Correspondence to Binbin Pang.

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Communicated by V. A. Zinoviev.

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Pang, B., Zhu, S., Yang, T. et al. BCH codes with larger dimensional hull. Des. Codes Cryptogr. 91, 3933–3951 (2023). https://doi.org/10.1007/s10623-023-01281-x

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  • DOI: https://doi.org/10.1007/s10623-023-01281-x

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