Doubly Even Self-Dual [40,20,8] Codes with Automorphism of an Odd Order

It is known that only the prime numbers 19, 7, 5, 3, and 2 can divide the order of the automorphism group of a doubly even self-dual [40,20,8] code. All these codes with automorphisms of order 19, 7, or 5 with twenty fixed points are already known. In the present paper, all doubly even self-dual [40,20,8] codes with automorphisms of order 5 are constructed. The number of these nonequivalent codes equals 45.