Cyclic self-dual codes
Neil J.A. Sloane, J. B. Thompson · IEEE Transactions on Information Theory · 1983
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 to2modulo4. 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 length14.