On the automorphisms of order 15 for a binary self-dual $$[96, 48, 20]$$[96,48,20] code

The structure of the binary self-dual codes invariant under the action of a cyclic group of order $$pq$$pq for odd primes $$p\ne q$$p≠q is considered. As an application we prove the nonexistence of an extremal self-dual $$[96, 48, 20]$$[96,48,20] code with an automorphism of order $$15$$15 which closes a gap in de la Cruz and Willems (IEEE Trans Inf Theory 57:6820–6823, 2011).

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