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The switching methods for constructing codes (binary, quaternary, q-ary, q>2) and an investigation of the nontrivial properties of codes are discussed in this paper. For each r, 0 ≤ r ≤ m, we present the class of quaternary linear codes [Lscr ][Rscr ][Mscr ](r,m) whose images under the Gray map are binary codes with the parameters of Reed-Muller RM(r,m) codes.
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