Binary images of some self-dual codes over GF(2m) with respect to trace-orthogonal basis

The note deals with a class of self-dual binary codes containing external doubly-even codes for lengths 8, 16, 24, 32, 40 and 64. For most of them, our construction also provides a simple method for calculating the distance of the code. To our knowledge, this is the first example of a (64, 32, 12) extermal doubly-even self-dual code.