Cyclic self-dual codes

It is shown that if the automorphism group of a binary self-dual code satisfies a certain condition then the code contains words of weight congruent to
2
modulo
4
. In particular, no cyclic binary self-dual code can have all its weights divisible by four. The number of cyclic binary self-dual codes of length n is determined, and the shortest nontrivial code in this class is shown to have length
14
.