具有l维Hermitian正交包的MDS码的构造

doi:10.12677/PM.2020.1011120

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具有l维Hermitian正交包的MDS码的构造
Construction of MDS Code with l-Dimensional Hermitian Hull

DOI: 10.12677/PM.2020.1011120, PDF, HTML, 下载: 466 浏览: 751
作者: 韩雨慧, 邱宇廷^*, 卢啸华：上海大学理学院，上海
关键词: MDS码；广义Reed-Solomon码；Hermitian正交包；MDS Codes； Generalized Reed-Solomon Codes； Hermitian Hull

摘要: 达到 Singleton 界的码称为极大距离可分码(简称为 MDS 码)，其纠错能力最强，在纠错码中有着非常广泛的应用。本文研究了MDS码的Hermitian正交包，利用广义 Reed-Solomon 码构造了具有l(l ≥ 1)维Hermitian正交包的MDS码。

Abstract: The codes achieving the Singleton bound are called maximum distance separable (for short MDS) codes, which have the strongest error correction ability and are widely applied in error-correcting code. In this paper, we study the Hermitian hulls of MDS codes. We use the generalized Reed-Solomon code to construct MDS codes with l-dimensional (l ≥ 1) Hermitian hull.

文章引用：韩雨慧, 邱宇廷, 卢啸华. 具有l维Hermitian正交包的MDS码的构造[J]. 理论数学, 2020, 10(11): 1015-1024. https://doi.org/10.12677/PM.2020.1011120

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