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Orbit and coset analysis of the Golay and related codes

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2 Author(s)
Conway, J. ; Math. Dept., Princeton Univ., NJ, USA ; Sloane, N.

Let b be a code of length n over a field F , with automorphism group G; bw denotes the subset of codewords of weight w. The goal is to classify the vectors of Fn into orbits under G and to determine their distances from the various subcodes b 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

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Information Theory, IEEE Transactions on  (Volume:36 ,  Issue: 5 )