On Extremal Self-Dual Codes of Length 96
Javier de la Cruz, Wolfgang M. Willems · IEEE Transactions on Information Theory · 2011
Let$C$be a binary extremal self-dual code of length 96. We prove that an automorphism of$C$of order 3 has 6 or no fixed points and an automorphism of order 5 has 6 fixed points. Moreover, if all automorphisms of order 3 are fixed point free then${\rm Aut}(C)$is solvable and its order divides$2^{5}3$or$2^{5}5$or${\rm Aut}(C)$is the alternating group${\rm A}_{5}$which is the only possible group of order 60. Furthermore,$\vert {\rm Aut}(C)\vert = 20$or$40$cannot occur.