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arXiv · 2202.11457

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

Guanmin Guo·Ruihu Li·Yang Liu·Hao Song
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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. In what follows, a new systematic approach is proposed to draw Hermitian self-dual (+)-GTRS codes. The necessary and sufficient conditions of a Hermitian self-dual (+)-GTRS code are presented.With this method, several classes of Hermitian self-dual MDS and NMDS codes are constructed.

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Guanmin Guo, Ruihu Li, Yang Liu, Hao Song. 2022-02-23. Duality of generalized twisted Reed-Solomon codes and Hermitian self-dual MDS or NMDS codes. https://arxiv.org/abs/2202.11457

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