Reed-Muller codes: Projections onto GF(4) and multilevel construction

Ofer Amrani*, Yair Be'ery

*Corresponding author for this work

Research output: Contribution to journalLetterpeer-review


A projection of binary Reed-Muller codes R(r, m) onto GF (4) m-2 is presented. For an R(r, m) code, this operation yields a linear quaternary code with the same length, dimension, and minimum distance as the Reed-Muller R(r-1, m-2) code. Based upon this projection, multilevel construction is given for R(r, m), where the constituent codes applied to the different levels are themselves the Reed-Muller codes R(r - 2, m - 2) and R(r, m - 2), as well as the aforementioned quaternary code. This construction of Reed-Muller codes is readily applicable for their efficient decoding.

Original languageEnglish
Pages (from-to)2560-2565
Number of pages6
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - Sep 2001


  • Mapping
  • Multilevel
  • Multistage
  • Projection
  • Reed-Muller codes


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