Hierarchical erasure correction of linear codes

Netanel Raviv, Moshe Schwartz, Rami Cohen, Yuval Cassuto

Research output: Contribution to journalArticlepeer-review

Abstract

Linear codes over finite extension fields have widespread applications in theory and practice. In some scenarios, the decoder has a sequential access to the codeword symbols, giving rise to a hierarchical erasure structure. In this paper we develop a mathematical framework for hierarchical erasures over extension fields, provide several bounds and constructions, and discuss potential applications in distributed storage and flash memories. Our results show intimate connection to Universally Decodable Matrices, as well as to Reed-Solomon and Gabidulin codes.

Original languageEnglish
Article number101743
JournalFinite Fields and Their Applications
Volume68
DOIs
StatePublished - 1 Dec 2020

Keywords

  • Erasure-correcting codes
  • Hierarchical erasures
  • Linear codes

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