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On the automorphisms of order 15 for a binary self-dual \([96, 48, 20]\) code. (English) Zbl 1352.94079

Summary: The structure of the binary self-dual codes invariant under the action of a cyclic group of order \(pq\) for odd primes \(p\neq q\) 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 [J. de la Cruz and W. Willems [IEEE Trans. Inf. Theory 57, No. 10, 6820–6823 (2011; doi:10.1109/TIT.2011.2155031)].

MSC:

94B05 Linear codes (general theory)
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
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References:

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