Reed–Muller codes are a family of error-correcting codes that are used in digital communication and data storage to detect and correct errors in transmitted or stored data. They are particularly known for their simple decoding algorithms and their good performance in terms of error correction capabilities.
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The binary Reed-Muller code evaluates Boolean polynomials of degree at most on . It has parametersThe dimension counts square-free monomials, and the minimum weight follows inductively from the decomposition .