A [72,36,16] doubly even code does not have an automorphism of order 11 (Corresp.)
W. Cary Huffman, Vassil Yorgov · IEEE Transactions on Information Theory · 1987
We prove that there does not exist a[72,36,16]doubly even code with an automorphism of order11. If such a code exists, it can be decomposed as a direct sum of two codes; one can be viewed as a self-dual[12,6,4]binary code and the other a self-dual[6,3,4]code overF_{1024}. This is shown to be impossible.