On Syndrome Decoding of Punctured Reed-Solomon and Gabidulin Codes

Hannes Bartz, Vladimir Sidorenko

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1 Citation (Scopus)

Abstract

Punctured Reed-Solomon (RS) and Gabidulin (G) codes over the field Fqm with locators from the subfield Fq can be represented as interleaving of m correspondent codes over the subfield Fq or can be considered as virtual interleaving of m correspondent codes over the field Fqm. Using a probabilistic unique syndrome decoder, m-interleaved or virtually interleaved codes can be decoded up to the same radius mm+1(d−1), where d is the code distance in Hamming metric for RS codes and in rank metric for G codes. We show that the correspondent decoders over the subfield Fq and the field Fqm are equivalent and conclude that in practice one should use a decoder over the subfield since it has less complexity.

Original languageEnglish
Pages (from-to)33-38
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume57
DOIs
Publication statusPublished - 1 Mar 2017
Externally publishedYes

Keywords

  • codes
  • Gabidulin
  • interleaved
  • punctured
  • Reed-Solomon
  • syndrome decoding

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