Involutory permutation automorphisms of binary linear codes

07/30/2022

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by   Fatma Altunbulak Aksu, et al.

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We investigate the properties of binary linear codes of even length whose permutation automorphism group is a cyclic group generated by an involution. Up to dimension or co-dimension 4, we show that there is no quasi group code whose permutation automorphism group is isomorphic to C_2. By generalizing the method we use to prove this result, we obtain results on the structure of putative extremal self-dual [72, 36, 16] and [96, 48, 20] codes in the presence of an involutory permutation automorphism.