Involutory permutation automorphisms of binary linear codes

07/30/2022

∙

by   Fatma Altunbulak Aksu, et al.

∙

Msgsusosyalmedya

∙

Gebze Technical University

∙

0

∙

share

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.