Four Times Extended Reed Solomon Codes, their Decoding and Application in EII Codes for Data Repair

Authors

  • Peter Farkas Institute of Multimedia ICT, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Bratislava, Slovakia
  • Martin Rakús Institute of Multimedia ICT, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Bratislava, Slovakia https://orcid.org/0000-0003-1564-1524
  • Katarína Farkasova Institute of Multimedia ICT, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Bratislava, Slovakia https://orcid.org/0009-0006-5254-1441
  • Frederik Pavelka Institute of Multimedia ICT, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Bratislava, Slovakia https://orcid.org/0009-0008-7364-2799
  • Ladislav Divinec Institute of Multimedia ICT, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Bratislava, Slovakia https://orcid.org/0000-0003-1058-724X

DOI:

https://doi.org/10.5755/j02.eie.43974

Keywords:

Digital storage, Error correction codes, Product codes, Reed Solomon 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  where  and  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  AMDS codes can be constructed over finite field  where the integer  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. 

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Published

2026-02-04

Issue

Early Access

Section

SYSTEM ENGINEERING, COMPUTER TECHNOLOGY

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By virtue of their appearance in this open access journal, papers are free to use with proper attribution in educational and other non-commercial settings with an acknowledgement of the initial publication in the journal.

How to Cite

Farkas, P., Rakús, M., Farkasova, K., Pavelka, F., & Divinec, L. (2026). Four Times Extended Reed Solomon Codes, their Decoding and Application in EII Codes for Data Repair. Elektronika Ir Elektrotechnika, 1(1). https://doi.org/10.5755/j02.eie.43974