On a Group Under Which Symmetric Reed-Muller Codes are Invariant
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911762095276032 |
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| author | Toplu, Sibel Kurt Arikan, Talha AydoğDu, Pinar Yayla, OğUz |
| author_facet | Toplu, Sibel Kurt Arikan, Talha AydoğDu, Pinar Yayla, OğUz |
| contents | The Reed-Muller codes are a family of error-correcting codes that have been widely studied in coding theory. In 2020, Wei Yan and Sian-Jheng Lin introduced a variant of Reed-Muller codes so called symmetric Reed-Muller codes. We investigate linear maps of the automorphism group of symmetric Reed-Muller codes and show that the set of these linear maps forms a subgroup of the general linear group, which is the automorphism group of punctured Reed-Muller codes. We provide a method to determine all the automorphisms in this subgroup explicitly for some special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11496 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Group Under Which Symmetric Reed-Muller Codes are Invariant Toplu, Sibel Kurt Arikan, Talha AydoğDu, Pinar Yayla, OğUz Information Theory 94B05, 11T71, 08A35, 11T06 The Reed-Muller codes are a family of error-correcting codes that have been widely studied in coding theory. In 2020, Wei Yan and Sian-Jheng Lin introduced a variant of Reed-Muller codes so called symmetric Reed-Muller codes. We investigate linear maps of the automorphism group of symmetric Reed-Muller codes and show that the set of these linear maps forms a subgroup of the general linear group, which is the automorphism group of punctured Reed-Muller codes. We provide a method to determine all the automorphisms in this subgroup explicitly for some special cases. |
| title | On a Group Under Which Symmetric Reed-Muller Codes are Invariant |
| topic | Information Theory 94B05, 11T71, 08A35, 11T06 |
| url | https://arxiv.org/abs/2401.11496 |