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

Abstract

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