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Large Hermitian hull GRS codes of any given length

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Abstract

The construction of Hermitian self-orthogonal generalized Reed-Solomon (GRS) codes of many specific lengths and large dimensions has been an active topic. The construction of Euclidean self-dual GRS codes and twisted generalized Reed-Solomon (TGRS) codes attracts some attentions. In this paper, we construct GRS \([n, k, n-k+1]_{q^2}\) codes (thus MDS codes) over \(\textbf{F}_{q^2}\) of the arbitrary length n satisfying \(n \le q^2+1\) and any given distance d satisfying \(d=O(q^2)\), such that the dimensions \(h \le k\) of its Hermitian hull is at least \(h=O(k)\). This work is a natural extension of previous constructions of Hermitian self-orthogonal GRS codes of many specific lengths. Our method can be used to construct large Hermitian hull MDS TGRS codes of the length \(n|(q^2-1)\).

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Acknowledgements

The author thanks two reviewers sincerely for helpful comments and suggestions.

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Authors and Affiliations

  1. College of Information Science and Technology/Cyber Security, Jinan University, Guangzhou, 510632, Guangdong, China

    Hao Chen

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  1. Hao Chen
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Correspondence to Hao Chen.

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Communicated by K.-U. Schmidt.

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The research of Hao Chen was supported by NSFC Grant 62032009.

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Chen, H. Large Hermitian hull GRS codes of any given length. Des. Codes Cryptogr. (2024). https://doi.org/10.1007/s10623-024-01369-y

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