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.
- Reed-Muller codes