A Repair Scheme for a Distributed Storage System Based on Multivariate Polynomials

Hiram H. López (), Gretchen L. Matthews () and Daniel Valvo ()
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Hiram H. López: Virginia Tech, Department of Mathematics
Gretchen L. Matthews: Virginia Tech, Department of Mathematics
Daniel Valvo: Virginia Tech, Department of Mathematics

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 761-775 from Springer

Abstract: Abstract A distributed storage system stores data across multiple nodes, with the primary objective of enabling efficient data recovery even in the event of node failures. The main goal of an exact repair scheme is to recover the data from a failed node by accessing and downloading information from the rest of the nodes. In a groundbreaking paper, Guruswami and Wootters (IEEE Trans Inf Theory 63(9):5684–5698, 2017) developed an exact repair scheme for a distributed storage system that is based on Reed-Solomon codes which depend on single-variable polynomials. In these notes, we extend the repair scheme to the family of distributed storage systems based on Reed-Muller codes which are linear codes based on multivariate polynomials. The repair scheme we propose repairs any single node failure and multiple node failures, provided the positions satisfy certain conditions.

Keywords: Reed-Solomon code; Reed-Muller code; Repair scheme; Distributed storage system (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16368-4_48

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