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. Then, a new systematic app...
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| Veröffentlicht in: | Cryptography and communications 2023-03, Vol.15 (2), p.383-395 |
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| creator | Guo, Guanmin Li, Ruihu Liu, Yang Song, Hao |
| description | 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. |
| doi_str_mv | 10.1007/s12095-022-00605-3 |
| format | Article |
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| subjects | Circuits Coding and Information Theory Combinatorial analysis Communications Engineering Computer Science Cryptography Data Structures and Information Theory Fields (mathematics) Information and Communication Mathematics of Computing Networks Reed-Solomon codes |
| title | Duality of generalized twisted Reed-Solomon codes and Hermitian self-dual MDS or NMDS codes |
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