On ternary self-dual codes of length 24
Jeffrey S. Leon, Vera S. Pless, Neil J.A. Sloane · IEEE Transactions on Information Theory · 1981
A partial classification is given of the self-dual codes of length 24 over GF (3). The main results are as follows: there are exactly two codes with minimum Hamming distanced=9; most of the codes haved=6and are indecomposable; one code withd=6has a trivial automorphism group (this is the first such self-dual code that has been found); the codes generated by the59inequivalent24 \times 24Hadamard matrices have been investigated and there appear to be only nine inequivalent codes (two withd=9and seven withd=6); and in all there are27decomposable codes, at least96indecomposable codes withd=6, and the total number of inequivalent codes is at least140.