Duality of generalized twisted Reed-Solomon codes and Hermitian self-dual MDS or NMDS codes
Guanmin Guo, Ruihu Li, Yang Liu, Hao Song
TL;DR
This paper explores the duality properties of generalized twisted Reed-Solomon codes and introduces a systematic method to construct Hermitian self-dual MDS and NMDS codes with potential cryptographic applications.
Contribution
It provides new conditions for Hermitian self-duality in GTRS codes and constructs several classes of such codes, advancing coding theory.
Findings
Duality properties of GTRS codes analyzed
A systematic approach for Hermitian self-dual (+)-GTRS codes proposed
New classes of Hermitian self-dual MDS and NMDS codes constructed
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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Taxonomy
TopicsCoding theory and cryptography · Cryptographic Implementations and Security · Error Correcting Code Techniques