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Duality of generalized twisted Reed-Solomon codes and Hermitian self-dual MDS or NMDS codes

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Abstract

Self-dual MDS and NMDS codes over finite fields are linear codes with significant combinatorial and cryptographic applications. In this paper, firstly, we investigate the duality properties of generalized twisted Reed-Solomon (abbreviated GTRS) codes in some special cases. Then, a new systematic approach is proposed to obtain Hermitian self-dual (+)-GTRS codes, and furthermore, necessary and sufficient conditions for a (+)-GTRS code to be Hermitian self-dual are presented. Finally, several classes of Hermitian self-dual MDS and NMDS codes are constructed with this method.

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Funding

This research was supported by the National Natural Science Foundation of China (Grant Nos. U21A20428 and 11901579), Natural Science Foundation of Shaanxi Province (Grant Nos. 2021JQ-335 and 2021JM-216), the Research Fund of Fundamentals Department of Air Force Engineering University (JK2022201), and Support fund for Excellent Doctoral Dissertation of Air Force Engineering University (Grant No. KGD083920015).

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  1. Fundamentals Department, Air Force Engineering University, 710051, **’an, Shaanxi, People’s Republic of China

    Guanmin Guo, Ruihu Li, Yang Liu & Hao Song

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  1. Guanmin Guo
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  2. Ruihu Li
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  4. Hao Song
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Correspondence to Guanmin Guo.

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Guo, G., Li, R., Liu, Y. et al. Duality of generalized twisted Reed-Solomon codes and Hermitian self-dual MDS or NMDS codes. Cryptogr. Commun. 15, 383–395 (2023). https://doi.org/10.1007/s12095-022-00605-3

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