Partial permutation decoding for several families of linear and z4-linear codes

Roland D. Barrolleta, Merce Villanueva

Research output: Contribution to journalArticleResearch

1 Citation (Scopus)

Abstract

© 1963-2012 IEEE. A general criterion to obtain s-PD-sets of minimum size s + 1 for partial permutation decoding, which enable correction up to s errors, for systematic codes over a finite field Fq and Z4-linear codes is provided. We show how this technique can be easily applied to linear cyclic codes over Fq, Z4-linear codes which are the Gray map image of a quaternary linear cyclic code, and some related codes such as quasi-cyclic codes. Furthermore, specific results for some linear and nonlinear binary codes, including simplex, Kerdock, Delsarte-Goethals, and extended dualized Kerdock codes are given. Finally, applying this technique, new s-PD-sets of size s + 1 for Z4-linear Hadamard codes of type 2γ 4δ, for all δ ≥ 4 and 1 < s ≤ 2δ - 3; and for Z4-linear simplex codes of type 4m, for all m ≥ 2 and 1 < s ≤ 2m+1 - 3, are also provided.
Original languageEnglish
Article number8364619
Pages (from-to)131-141
JournalIEEE Transactions on Information Theory
Volume65
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • cyclic codes
  • Hadamard codes
  • Kerdock codes
  • nonlinear codes
  • Permutation decoding
  • quasi-cyclic codes
  • simplex codes
  • Z4-linear codes

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