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Involutory permutation automorphisms of binary linear codes (2208.00299v1)
Published 30 Jul 2022 in cs.IT and math.IT
Abstract: 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.