Linear exact repair schemes for free MDS and Reed–Solomon codes over Galois rings.
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| Title: | Linear exact repair schemes for free MDS and Reed–Solomon codes over Galois rings. |
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| Authors: | Bossaller, Daniel P.1 (AUTHOR) daniel.bossaller@uah.edu, López, Hiram H.2 (AUTHOR) hhlopez@vt.edu |
| Source: | Journal of Algebra & Its Applications. Nov/Dec2025, Vol. 24 Issue 13/14, p1-17. 17p. |
| Subjects: | Reed-Solomon codes, Linear codes, Finite fields, Data recovery, Storage |
| Abstract: | Codes over rings, especially over Galois rings, have been extensively studied for nearly three decades due to their similarity to linear codes over finite fields. A distributed storage system uses a linear code to encode a large file across several nodes. If one of the nodes fails, a linear exact repair scheme efficiently recovers the failed node by accessing and downloading data from the rest of the servers of the storage system. In this paper, we develop a linear repair scheme for free maximum distance separable codes, which coincide with free maximum distance with respect to the rank codes over Galois rings. In particular, we give a linear repair scheme for full-length Reed–Solomon codes over a Galois ring. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Algebra & Its Applications is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 189646258 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Linear exact repair schemes for free MDS and Reed–Solomon codes over Galois rings. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bossaller%2C+Daniel+P%2E%22">Bossaller, Daniel P.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> daniel.bossaller@uah.edu</i><br /><searchLink fieldCode="AR" term="%22López%2C+Hiram+H%2E%22">López, Hiram H.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> hhlopez@vt.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Algebra+%26+Its+Applications%22">Journal of Algebra & Its Applications</searchLink>. Nov/Dec2025, Vol. 24 Issue 13/14, p1-17. 17p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Reed-Solomon+codes%22">Reed-Solomon codes</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+codes%22">Linear codes</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+fields%22">Finite fields</searchLink><br /><searchLink fieldCode="DE" term="%22Data+recovery%22">Data recovery</searchLink><br /><searchLink fieldCode="DE" term="%22Storage%22">Storage</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Codes over rings, especially over Galois rings, have been extensively studied for nearly three decades due to their similarity to linear codes over finite fields. A distributed storage system uses a linear code to encode a large file across several nodes. If one of the nodes fails, a linear exact repair scheme efficiently recovers the failed node by accessing and downloading data from the rest of the servers of the storage system. In this paper, we develop a linear repair scheme for free maximum distance separable codes, which coincide with free maximum distance with respect to the rank codes over Galois rings. In particular, we give a linear repair scheme for full-length Reed–Solomon codes over a Galois ring. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Algebra & Its Applications is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=189646258 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/S0219498825410312 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 1 Subjects: – SubjectFull: Reed-Solomon codes Type: general – SubjectFull: Linear codes Type: general – SubjectFull: Finite fields Type: general – SubjectFull: Data recovery Type: general – SubjectFull: Storage Type: general Titles: – TitleFull: Linear exact repair schemes for free MDS and Reed–Solomon codes over Galois rings. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bossaller, Daniel P. – PersonEntity: Name: NameFull: López, Hiram H. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov/Dec2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 02194988 Numbering: – Type: volume Value: 24 – Type: issue Value: 13/14 Titles: – TitleFull: Journal of Algebra & Its Applications Type: main |
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