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arXiv · 1801.05848

Random Construction of Partial MDS Codes

Alessandro Neri·Anna-Lena Horlemann-Trautmann
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Abstract

This work deals with partial MDS (PMDS) codes, a special class of locally repairable codes, used for distributed storage system. We first show that a known construction of these codes, using Gabidulin codes, can be extended to use any maximum rank distance code. Then we define a standard form for the generator matrices of PMDS codes and use this form to give an algebraic description of PMDS generator matrices. This implies that over a sufficiently large finite field a randomly chosen generator matrix in PMDS standard form generates a PMDS code with high probability. This also provides sufficient conditions on the field size for the existence of PMDS codes.

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Alessandro Neri, Anna-Lena Horlemann-Trautmann. 2018-01-17. Random Construction of Partial MDS Codes. https://arxiv.org/abs/1801.05848

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