Classification of some families of quaternary Reed-Muller codes

Jaume Pernas, Jaume Pujol, Mercè Villanueva

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

Recently, new families of quaternary linear Reed-Muller codes have been introduced. They satisfy that, after the Gray map, the corresponding ℤ4-linear codes have the same parameters and properties as the codes of the binary linear Reed-Muller family. A structural invariant, the dimension of the kernel, for binary codes is used to classify completely these ℤ4-linear codes. The dimension of the kernel for these ℤ4-linear codes is established generalizing the known results about the dimension of the kernel for ℤ4-linear Hadamard and ℤ4-linear extended 1-perfect codes. © 2011 IEEE.
Original languageEnglish
Article number6006598
Pages (from-to)6043-6051
JournalIEEE Transactions on Information Theory
Volume57
Issue number9
DOIs
Publication statusPublished - 1 Sep 2011

Keywords

  • ℤ -linear codes 4
  • kernel
  • quaternary codes
  • Reed-Muller codes

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