On extremal self-dual codes of length 120

Abstract

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