On extremal self-dual codes of length 120
We prove that the only primes which may divide the order of the automorphism group of a putative binary self-dual doubly-even \([120, 60, 24]\) code are \(2, 3, 5, 7, 19, 23\) and \(29\). Furthermore we prove that automorphisms of prime order \(p \ge 5\) have a unique cycle structure. Parts of the results are based on computer computations.
automorphism group extremal self-dual doubly-even code 94b05