Constructions of High-Rate Minimum Storage Regenerating Codes over Small Fields

Netanel Raviv, Natalia Silberstein, Tuvi Etzion

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


regenerating (MSR) codes is presented. Based on this technique, three explicit constructions of MSR codes are given. The first two constructions provide access-optimal MSR codes, with two and three parities, respectively, which attain the subpacketization bound for access-optimal codes. The third construction provides longer MSR codes with three parities (i.e., codes with larger number of systematic nodes). This improvement is achieved at the expense of the access-optimality and the field size. In addition to a minimum storage in a node, all three constructions allow the entire data to be recovered from a minimal number of storage nodes. That is, given storage ℓ in each node, the entire stored data can be recovered from any 2 log2 ℓ for two parity nodes, and either 3 log3ℓ or 4 log3ℓ for three parities. Second, in the first two constructions, a helper node accesses the minimum number of its symbols for repair of a failed node (access-optimality). The goal of this paper is to provide a construction of such optimal codes over the smallest possible finite fields. The generator matrix of these codes is based on perfect matchings of complete graphs and hypergraphs, and on a rational canonical form of matrices. For two parities, the field size is reduced by a factor of two for access-optimal codes compared to previous constructions. For three parities, in the first construction a field size of at least 6log3ℓ + 1 (or 3 log3ℓ + 1 for fields with characteristic 2) is sufficient, and in the second construction the field size is larger, yet linear in log3ℓ . Both constructions with three parities provide a significant improvement over previous works due to either decreased field size or lower subpacketization.

Original languageEnglish
Article number7833084
Pages (from-to)2015-2038
Number of pages24
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - 1 Apr 2017


  • MSR codes
  • Regenerating codes
  • access-optimal codes
  • perfect matchings
  • subspace condition

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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