Recently Vera Pless, N. J. A. Sloane, and I completed the classification of ternary self-dual codes of length 20 . We produced most of the codes by building on known codes of shorter length (the techniques are outlined and applied to codes of length 16 in a paper of Conway, Pless, and Sloane ). However, we used a different method for finding those codes having minimum weight 6. It is based on regarding the words of weight 6 as binary words and then examining the resulting set of binary vectors. The second section of this paper contains a summary of the results used in this approach; a detailed exposition will appear elsewhere . Since the method links binary and ternary codes, the third section presents applications to the two most conspicuous of such linked codes, the ternary extended Golay code of length 12 and the binary extended Golay code of length 24.
Symplectic Form Linear Code Minimum Weight Affine Plane Golay Code
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Pless, V., Sloane, N. J. A., and Ward, H. N., Ternary codes of minimum weight 6 and the classification of the self-dual codes of length 20. IEEE Trans. Information TheoryIT-26 (1980), 305–316.MathSciNetCrossRefGoogle Scholar