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Basic procedures for Cyclic, Hamming, Binary Reed-Muller, BCH, and Golay codes We construct the parity-check matrix and generator matrix of the cyclic code of length n over GF(p), the Hamming code over GF(p), the binary 1st order Reed-Muller code (which is length n=2m, dimension m+1, minimum distance 2m-1), the ternary (11, 6)-Golay (which is perfect, minimum distance 5, and 2-error-correcting), ...