Involutory permutation automorphisms of binary linear codes
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866915196591669248 |
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| author | Aksu, Fatma Altunbulak Hafezieh, Roghayeh Tuvay, İpek |
| author_facet | Aksu, Fatma Altunbulak Hafezieh, Roghayeh Tuvay, İpek |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_00299 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Involutory permutation automorphisms of binary linear codes Aksu, Fatma Altunbulak Hafezieh, Roghayeh Tuvay, İpek Information Theory 94B05, 11T71, 20B05 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. |
| title | Involutory permutation automorphisms of binary linear codes |
| topic | Information Theory 94B05, 11T71, 20B05 |
| url | https://arxiv.org/abs/2208.00299 |