On extremal self-dual ternary codes of length 48

The notion of an extremal self-dual code has been introduced in 1 . As Gleason 2 remarks onemay use invariance properties of the weight enumerator of a self-dual code to deduce upper bounds on the minimum distance. Extremal codes are self-dual codes that achieve these bounds. The most wanted extremal code is a binary self-dual doubly even code of length 72 and minimum distance 16. One frequently used strategy is to classify extremal codes with a given automorphism, see 3, 4 for the first papers on this subject. Ternary codes with a given automorphism have been studied in 5 . Theminimumdistance d C : min{wt c | 0/ c ∈ C} of a self-dual ternary code C C⊥ ≤ Fn3 of length n is bounded by