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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.
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]
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Database: Engineering Source
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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]
ISSN:13921215
DOI:10.5755/j02.eie.43974