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 [Formula: see text]. By generalizing the method we use to prove this result, we obtain results on the structure of putative extremal self-dual [Formula: see text] and [Formula: see text] codes in the presence of an involutory permutation automorphism.
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