Duality of generalized twisted Reed-Solomon codes and Hermitian self-dual MDS or NMDS codes
Information Theory
2022-02-24 v1 math.IT
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.
Keywords
Cite
@article{arxiv.2202.11457,
title = {Duality of generalized twisted Reed-Solomon codes and Hermitian self-dual MDS or NMDS codes},
author = {Guanmin Guo and Ruihu Li and Yang Liu and Hao Song},
journal= {arXiv preprint arXiv:2202.11457},
year = {2022}
}
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13 pages, 1 table