Orbit and coset analysis of the Golay and related codes
John H. Conway, Neil J.A. Sloane · IEEE Transactions on Information Theory · 1990
Let b be a code of length n over a field F, with automorphism group G; b/sub w/ denotes the subset of codewords of weight w. The goal is to classify the vectors of F/sup n/ into orbits under G and to determine their distances from the various subcodes b/sub w/. This is done for the first-order Reed-Muller, Nordstrom-Robinson, and Hamming codes of length 16, the Golay and shortened Golay codes of lengths 22, 23, 24, and the ternary Golay code of length 12.>