Bibliographic Details
| Title: |
Linear exact repair schemes for free MDS and Reed–Solomon codes over Galois rings. |
| 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] |
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| Database: |
Engineering Source |
