On the affine permutation group of certain decreasing Cartesian codes
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909201145528320 |
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| author | Camps-Moreno, Eduardo López, Hiram H. Sarmiento, Eliseo Soprunov, Ivan |
| author_facet | Camps-Moreno, Eduardo López, Hiram H. Sarmiento, Eliseo Soprunov, Ivan |
| contents | A decreasing Cartesian code is defined by evaluating a monomial set closed under divisibility on a Cartesian set. Some well-known examples are the Reed-Solomon, Reed-Muller, and (some) toric codes. The affine permutations consist of the permutations of the code that depend on an affine transformation. In this work, we study the affine permutations of some decreasing Cartesian codes, including the case when the Cartesian set has copies of multiplicative or additive subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08112 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the affine permutation group of certain decreasing Cartesian codes Camps-Moreno, Eduardo López, Hiram H. Sarmiento, Eliseo Soprunov, Ivan Combinatorics A decreasing Cartesian code is defined by evaluating a monomial set closed under divisibility on a Cartesian set. Some well-known examples are the Reed-Solomon, Reed-Muller, and (some) toric codes. The affine permutations consist of the permutations of the code that depend on an affine transformation. In this work, we study the affine permutations of some decreasing Cartesian codes, including the case when the Cartesian set has copies of multiplicative or additive subgroups. |
| title | On the affine permutation group of certain decreasing Cartesian codes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.08112 |