Four Times Extended Reed Solomon Codes, their Decoding and Application in EII Codes for Data Repair.
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| Title: | Four Times Extended Reed Solomon Codes, their Decoding and Application in EII Codes for Data Repair. |
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| Authors: | Farkas, Peter1,2 p.farkas@ieee.org, Rakus, Martin1 martin.rakus@stuba.sk, Farkasova, Katarina1 katarina.farkasova@stuba.sk, Pavelka, Frederik1 frederik.pavelka@stuba.sk, Divinec, Ladislav1 ladislav.divinec@stuba.sk |
| Source: | Electronics & Electrical Engineering. 2026, Vol. 32 Issue 1, p55-63. 9p. |
| Subjects: | Reed-Solomon codes, Data recovery, Finite fields, Block codes, Distributed databases, Error-correcting codes |
| Abstract: | Data recovery in distributed and general storage systems requires a broad range of regenerating codes with different properties such as locality, availability, scalability, etc. The main goal of this paper is to enrich this palette with four times extended Reed Solomon (RS) codes. Recently, it was shown that RS codes can be extended five times, when constructed over finite fields GF(q), where q = 2ξ and ξ ≥ 3 is an odd integer. These codes are almost maximum distance separable (AMDS), and they are reaching upper bounds on code distance in known tables on the best linear block codes. However, such codes have limitations for practical applications since has to be an odd integer. To overcome this limitation, four times extended RS codes are presented in this paper. These [q + 3, q - 1, 4] AMDS codes can be constructed over finite field GF (2ξ), where the integer μ ≥3 is arbitrary. They can be used in numerous different constructions of product codes, Extended Product codes, Integrated Interleaved codes, Extended Integrated Interleaved codes, Staircase codes, and others, which are suitable for data recovery in storage systems. [ABSTRACT FROM AUTHOR] |
| Copyright of Electronics & Electrical Engineering is the property of Electronics & Electrical Engineering 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 |
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| Items | – Name: Title Label: Title Group: Ti Data: Four Times Extended Reed Solomon Codes, their Decoding and Application in EII Codes for Data Repair. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Farkas%2C+Peter%22">Farkas, Peter</searchLink><relatesTo>1,2</relatesTo><i> p.farkas@ieee.org</i><br /><searchLink fieldCode="AR" term="%22Rakus%2C+Martin%22">Rakus, Martin</searchLink><relatesTo>1</relatesTo><i> martin.rakus@stuba.sk</i><br /><searchLink fieldCode="AR" term="%22Farkasova%2C+Katarina%22">Farkasova, Katarina</searchLink><relatesTo>1</relatesTo><i> katarina.farkasova@stuba.sk</i><br /><searchLink fieldCode="AR" term="%22Pavelka%2C+Frederik%22">Pavelka, Frederik</searchLink><relatesTo>1</relatesTo><i> frederik.pavelka@stuba.sk</i><br /><searchLink fieldCode="AR" term="%22Divinec%2C+Ladislav%22">Divinec, Ladislav</searchLink><relatesTo>1</relatesTo><i> ladislav.divinec@stuba.sk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Electronics+%26+Electrical+Engineering%22">Electronics & Electrical Engineering</searchLink>. 2026, Vol. 32 Issue 1, p55-63. 9p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Reed-Solomon+codes%22">Reed-Solomon codes</searchLink><br /><searchLink fieldCode="DE" term="%22Data+recovery%22">Data recovery</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+fields%22">Finite fields</searchLink><br /><searchLink fieldCode="DE" term="%22Block+codes%22">Block codes</searchLink><br /><searchLink fieldCode="DE" term="%22Distributed+databases%22">Distributed databases</searchLink><br /><searchLink fieldCode="DE" term="%22Error-correcting+codes%22">Error-correcting codes</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Data recovery in distributed and general storage systems requires a broad range of regenerating codes with different properties such as locality, availability, scalability, etc. The main goal of this paper is to enrich this palette with four times extended Reed Solomon (RS) codes. Recently, it was shown that RS codes can be extended five times, when constructed over finite fields GF(q), where q = 2ξ and ξ ≥ 3 is an odd integer. These codes are almost maximum distance separable (AMDS), and they are reaching upper bounds on code distance in known tables on the best linear block codes. However, such codes have limitations for practical applications since has to be an odd integer. To overcome this limitation, four times extended RS codes are presented in this paper. These [q + 3, q - 1, 4] AMDS codes can be constructed over finite field GF (2ξ), where the integer μ ≥3 is arbitrary. They can be used in numerous different constructions of product codes, Extended Product codes, Integrated Interleaved codes, Extended Integrated Interleaved codes, Staircase codes, and others, which are suitable for data recovery in storage systems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Electronics & Electrical Engineering is the property of Electronics & Electrical Engineering 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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.5755/j02.eie.43974 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 9 StartPage: 55 Subjects: – SubjectFull: Reed-Solomon codes Type: general – SubjectFull: Data recovery Type: general – SubjectFull: Finite fields Type: general – SubjectFull: Block codes Type: general – SubjectFull: Distributed databases Type: general – SubjectFull: Error-correcting codes Type: general Titles: – TitleFull: Four Times Extended Reed Solomon Codes, their Decoding and Application in EII Codes for Data Repair. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Farkas, Peter – PersonEntity: Name: NameFull: Rakus, Martin – PersonEntity: Name: NameFull: Farkasova, Katarina – PersonEntity: Name: NameFull: Pavelka, Frederik – PersonEntity: Name: NameFull: Divinec, Ladislav IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13921215 Numbering: – Type: volume Value: 32 – Type: issue Value: 1 Titles: – TitleFull: Electronics & Electrical Engineering Type: main |
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