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^*

^*Corresponding author for this work

Software Engineering Institute

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Article number	102084
Journal	Finite Fields and their Applications
Volume	83
DOIs	https://doi.org/10.1016/j.ffa.2022.102084
State	Published - Oct 2022

Keywords

Galois hull
Generalized Reed-Solomon code
Goppa code

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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.",

keywords = "Galois hull, Generalized Reed-Solomon code, Goppa code",

author = "Yansheng Wu and Chengju Li and Shangdong Yang",

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year = "2022",

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AU - Wu, Yansheng

AU - Li, Chengju

AU - Yang, Shangdong

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Y1 - 2022/10

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

U2 - 10.1016/j.ffa.2022.102084

DO - 10.1016/j.ffa.2022.102084

M3 - 文章

AN - SCOPUS:85133589903

SN - 1071-5797

VL - 83

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

M1 - 102084

ER -

New Galois hulls of generalized Reed-Solomon codes

Abstract

Keywords

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