17 does not divide the order of the group of a (72,36,16) doubly even code (Corresp.)
Vera S. Pless, J. B. Thompson · IEEE Transactions on Information Theory · 1982
It is an interesting open question whether an extremal (72, 36, 16) doubly even code C exists. In [3] the odd prime numbers which can divide the order of the group of C were determined. The largest of these, 23, was eliminated by finding weight 12 vectors in 384 codes [8]. The next largest prime remaining is 17. It is shown that 17 is also not possible by reducing the problem to the consideration of16.17^{3}codes and then finding a weight 12 vector, by computer, in each of these codes.