Reed–Muller Codes
Reed–Muller may refer to: * Reed–Muller code * Reed–Muller expansion In Boolean logic, a Reed–Muller expansion (or Davio expansion) is a decomposition of a Boolean function. For a Boolean function f(x_1,\ldots,x_n) : \mathbb^n \to \mathbb we call : \begin f_(x) & = f(x_1,\ldots,x_,1,x_,\ldots,x_n) \\ f_(x)& = ...

Reed–Muller Code
Reed–Muller codes are error-correcting codes that are used in wireless communications applications, particularly in deep-space communication. Moreover, the proposed 5G standard relies on the closely related polar codes for error correction in the control channel. Due to their favorable theoretical and mathematical properties, Reed–Muller codes have also been extensively studied in theoretical computer science. Reed–Muller codes generalize the Reed–Solomon codes and the Walsh–Hadamard code. Reed–Muller codes are linear block codes that are locally testable, locally decodable, and list decodable. These properties make them particularly useful in the design of probabilistically checkable proofs. Traditional Reed–Muller codes are binary codes, which means that messages and codewords are binary strings. When ''r'' and ''m'' are integers with 0 ≤ ''r'' ≤ ''m'', the Reed–Muller code with parameters ''r'' and ''m'' is denoted as RM(''r'', ''m''). When ask ...
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