New extremal self-dual codes of length 68

We give two computational results on binary self-dual codes. A number of extremal singly-even self-dual [68, 34, 12] codes with weight enumerators not known to exist, are constructed. For k/spl les/10, the relationship between extremal doubly-even self-dual codes of length 24 k, and certain singly-even self-dual codes of length 24 k-2 is presented.