High Quality Content by WIKIPEDIA articles! Reed–Muller codes are a family of linear error-correcting codes used in communications. They are named after their discoverers, Irving S. Reed and D. E. Muller. Muller discovered the codes, and Reed proposed the majority logic decoding for the first time. A first order Reed–Muller code is equivalent to a Hadamard code. Reed–Muller codes are listed as RM(d, r), where d is the order of the code, and r is parameter related to the length of code, n = 2 r. RM codes are related to binary functions on field GF(2 r) over the elements [0, 1].

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