Involutory permutation automorphisms of binary linear codes

Fatma Altunbulak Aksu; Roghayeh Hafezieh; İpek Tuvay

doi:10.1142/s0219498825501373

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arXiv · 2208.00299

Involutory permutation automorphisms of binary linear codes

Fatma Altunbulak Aksu·Roghayeh Hafezieh·İpek Tuvay

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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.

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Fatma Altunbulak Aksu, Roghayeh Hafezieh, İpek Tuvay. 2022-07-30. Involutory permutation automorphisms of binary linear codes. https://doi.org/10.1142/s0219498825501373

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