On ternary self-dual codes of length 24

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 distance
d=9
; most of the codes have
d=6
and are indecomposable; one code with
d=6
has a trivial automorphism group (this is the first such self-dual code that has been found); the codes generated by the
59
inequivalent
24 \times 24
Hadamard matrices have been investigated and there appear to be only nine inequivalent codes (two with
d=9
and seven with
d=6)
; and in all there are
27
decomposable codes, at least
96
indecomposable codes with
d=6
, and the total number of inequivalent codes is at least
140
.