Random construction of partial MDS codes

Abstract

This work deals with partial MDS (PMDS) codes, a special class of locally repairable codes, used for distributed storage systems. 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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Correspondence to Anna-Lena Horlemann-Trautmann.

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A. Neri was partially supported by Swiss National Science Foundation Grants No. 169510 and 187711.

Communicated by V. A. Zinoviev.

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Neri, A., Horlemann-Trautmann, AL. Random construction of partial MDS codes. Des. Codes Cryptogr. 88, 711–725 (2020). https://doi.org/10.1007/s10623-019-00705-x

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Keywords

  • Distributed storage
  • Partial MDS codes
  • Maximally recoverable codes