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

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 sys...

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Bibliographic Details
Published in:arXiv.org 2022-02
Main Authors: Guo, Guanmin, Li, Ruihu, Liu, Yang, Song, Hao
Format: Article
Language:English
Subjects:
Binary system
Codes
Combinatorial analysis
Cryptography
Fields (mathematics)
Reed-Solomon codes
Online Access:Get full text
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Summary: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.
ISSN:2331-8422