New Galois hulls of generalized Reed-Solomon codes

Yansheng Wu; Chengju Li; Shangdong Yang

doi:10.1016/j.ffa.2022.102084

New Galois hulls of generalized Reed-Solomon codes

Yansheng Wu
, Chengju Li
, Shangdong Yang^*

^*此作品的通讯作者

软件工程学院

Nanjing University of Posts and Telecommunications
Xidian University
Southeast University, Nanjing

科研成果: 期刊稿件 › 文章 › 同行评审

11 引用（Scopus）

摘要

Most recently, Gao et al. found a nice method to investigate the Euclidean hulls of generalized Reed-Solomon codes in terms of Goppa codes. In this note, we extend the results to general Galois hull. We prove that the Galois hulls of some GRS codes are still GRS codes. We also give some examples on Galois LCD and self-dual MDS codes. Compare with known results, the Galois hulls of GRS codes obtained in this work have flexible parameters.

源语言	英语
文章编号	102084
期刊	Finite Fields and their Applications
卷	83
DOI	https://doi.org/10.1016/j.ffa.2022.102084
出版状态	已出版 - 10月 2022

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10.1016/j.ffa.2022.102084

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title = "New Galois hulls of generalized Reed-Solomon codes",

abstract = "Most recently, Gao et al. found a nice method to investigate the Euclidean hulls of generalized Reed-Solomon codes in terms of Goppa codes. In this note, we extend the results to general Galois hull. We prove that the Galois hulls of some GRS codes are still GRS codes. We also give some examples on Galois LCD and self-dual MDS codes. Compare with known results, the Galois hulls of GRS codes obtained in this work have flexible parameters.",

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AU - Li, Chengju

AU - Yang, Shangdong

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N2 - Most recently, Gao et al. found a nice method to investigate the Euclidean hulls of generalized Reed-Solomon codes in terms of Goppa codes. In this note, we extend the results to general Galois hull. We prove that the Galois hulls of some GRS codes are still GRS codes. We also give some examples on Galois LCD and self-dual MDS codes. Compare with known results, the Galois hulls of GRS codes obtained in this work have flexible parameters.

AB - Most recently, Gao et al. found a nice method to investigate the Euclidean hulls of generalized Reed-Solomon codes in terms of Goppa codes. In this note, we extend the results to general Galois hull. We prove that the Galois hulls of some GRS codes are still GRS codes. We also give some examples on Galois LCD and self-dual MDS codes. Compare with known results, the Galois hulls of GRS codes obtained in this work have flexible parameters.

KW - Galois hull

KW - Generalized Reed-Solomon code

KW - Goppa code

UR - https://www.scopus.com/pages/publications/85133589903

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DO - 10.1016/j.ffa.2022.102084

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ER -

New Galois hulls of generalized Reed-Solomon codes

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