Generalized Reed-Solomon codes over number fields and exact gradient coding
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.
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.2024464?viewType=HTML |
| _version_ | 1827312500004093952 |
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| author | Irwansyah Intan Muchtadi-Alamsyah Fajar Yuliawan Muhammad Irfan Hidayat |
| author_facet | Irwansyah Intan Muchtadi-Alamsyah Fajar Yuliawan Muhammad Irfan Hidayat |
| author_sort | Irwansyah |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T21:44:23Z |
| format | Article |
| id | doaj.art-1ba4cf8d50ad49f7992fd734b0b3cf7c |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T21:44:23Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-1ba4cf8d50ad49f7992fd734b0b3cf7c2024-03-21T01:14:29ZengAIMS PressAIMS Mathematics2473-69882024-03-01949508951810.3934/math.2024464Generalized Reed-Solomon codes over number fields and exact gradient codingIrwansyah0Intan Muchtadi-Alamsyah1Fajar Yuliawan 2Muhammad Irfan Hidayat31. Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Mataram, Indonesia2. Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia2. Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia2. Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, IndonesiaThis 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.https://aimspress.com/article/doi/10.3934/math.2024464?viewType=HTMLgeneralized reed-solomon codesgeneralized quasi-cyclic codesnumber fieldsgalois groupexact gradient coding |
| spellingShingle | Irwansyah Intan Muchtadi-Alamsyah Fajar Yuliawan Muhammad Irfan Hidayat Generalized Reed-Solomon codes over number fields and exact gradient coding AIMS Mathematics generalized reed-solomon codes generalized quasi-cyclic codes number fields galois group exact gradient coding |
| title | Generalized Reed-Solomon codes over number fields and exact gradient coding |
| title_full | Generalized Reed-Solomon codes over number fields and exact gradient coding |
| title_fullStr | Generalized Reed-Solomon codes over number fields and exact gradient coding |
| title_full_unstemmed | Generalized Reed-Solomon codes over number fields and exact gradient coding |
| title_short | Generalized Reed-Solomon codes over number fields and exact gradient coding |
| title_sort | generalized reed solomon codes over number fields and exact gradient coding |
| topic | generalized reed-solomon codes generalized quasi-cyclic codes number fields galois group exact gradient coding |
| url | https://aimspress.com/article/doi/10.3934/math.2024464?viewType=HTML |
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