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Research Article | Open Access

Generalized Reed-Solomon codes over number fields and exact gradient coding

Irwansyah1( ), Intan Muchtadi-Alamsyah2, Fajar Yuliawan2, Muhammad Irfan Hidayat2
Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Indonesia
Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
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Abstract

This paper describes generalized Reed-Solomon (GRS) codes over number fields that are invariant under certain permutations. We call these codes generalized quasi-cyclic (GQC) GRS codes. Moreover, we describe an application of GQC GRS codes over number fields to exact gradient coding.

Keywords

generalized Reed-Solomon codesgeneralized quasi-cyclic codesnumber fieldsGalois groupexact gradient coding
CLC number: 11T71, 68P30

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 9508-9518
DOI: 10.3934/math.2024464

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Cite this article:
Irwansyah, Muchtadi-Alamsyah I, Yuliawan F, et al. Generalized Reed-Solomon codes over number fields and exact gradient coding. AIMS Mathematics, 2024, 9(4): 9508-9518. https://doi.org/10.3934/math.2024464

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Received: 31 December 2023
Revised: 09 February 2024
Accepted: 20 February 2024
Published: 15 April 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)