A [72,36,16] doubly even code does not have an automorphism of order 11 (Corresp.)

We prove that there does not exist a
[72,36,16]
doubly even code with an automorphism of order
11
. 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 over
F_{1024}
. This is shown to be impossible.