Gray isometries for finite $p$-groups
We construct two classes of Gray maps, called type-I Gray map and type-II Gray map, for a finite $p$-group $G$. Type-I Gray maps are constructed based on the existence of a Gray map for a maximal subgroup $H$ of $G$. When $G$ is a semidirect product of two finite $p$-groups $H$ and $K$, both $H$ and...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2013-03-01
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| Series: | Transactions on Combinatorics |
| Subjects: | |
| Online Access: | http://www.combinatorics.ir/?_action=showPDF&article=2762&_ob=c4b07819ea8798454cff55f3b453576c&fileName=full_text.pdf. |
| _version_ | 1818266359220404224 |
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| author | Reza Sobhani |
| author_facet | Reza Sobhani |
| author_sort | Reza Sobhani |
| collection | DOAJ |
| description | We construct two classes of Gray maps, called type-I Gray map and type-II Gray map, for a finite $p$-group $G$. Type-I Gray maps are constructed based on the existence of a Gray map for a maximal subgroup $H$ of $G$. When $G$ is a semidirect product of two finite $p$-groups $H$ and $K$, both $H$ and $K$ admit Gray maps and the corresponding homomorphism $psi:Hlongrightarrow {rm Aut}(K)$ is compatible with the Gray map of $K$ in a sense which we will explain, we construct type-II Gray maps for $G$. Finally, we consider group codes over the dihedral group $D_8$ of order 8 given by the set of their generators, and derive a representation and an encoding procedure for such codes. |
| first_indexed | 2024-12-12T20:05:27Z |
| format | Article |
| id | doaj.art-ea159ac4605a46adbe7a8ab6c59e78b7 |
| institution | Directory Open Access Journal |
| issn | 2251-8657 2251-8665 |
| language | English |
| last_indexed | 2024-12-12T20:05:27Z |
| publishDate | 2013-03-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | Transactions on Combinatorics |
| spelling | doaj.art-ea159ac4605a46adbe7a8ab6c59e78b72022-12-22T00:13:38ZengUniversity of IsfahanTransactions on Combinatorics2251-86572251-86652013-03-01211726Gray isometries for finite $p$-groupsReza SobhaniWe construct two classes of Gray maps, called type-I Gray map and type-II Gray map, for a finite $p$-group $G$. Type-I Gray maps are constructed based on the existence of a Gray map for a maximal subgroup $H$ of $G$. When $G$ is a semidirect product of two finite $p$-groups $H$ and $K$, both $H$ and $K$ admit Gray maps and the corresponding homomorphism $psi:Hlongrightarrow {rm Aut}(K)$ is compatible with the Gray map of $K$ in a sense which we will explain, we construct type-II Gray maps for $G$. Finally, we consider group codes over the dihedral group $D_8$ of order 8 given by the set of their generators, and derive a representation and an encoding procedure for such codes.http://www.combinatorics.ir/?_action=showPDF&article=2762&_ob=c4b07819ea8798454cff55f3b453576c&fileName=full_text.pdf.Finite groupCodeGray mapIsometry |
| spellingShingle | Reza Sobhani Gray isometries for finite $p$-groups Transactions on Combinatorics Finite group Code Gray map Isometry |
| title | Gray isometries for finite $p$-groups |
| title_full | Gray isometries for finite $p$-groups |
| title_fullStr | Gray isometries for finite $p$-groups |
| title_full_unstemmed | Gray isometries for finite $p$-groups |
| title_short | Gray isometries for finite $p$-groups |
| title_sort | gray isometries for finite p groups |
| topic | Finite group Code Gray map Isometry |
| url | http://www.combinatorics.ir/?_action=showPDF&article=2762&_ob=c4b07819ea8798454cff55f3b453576c&fileName=full_text.pdf. |
| work_keys_str_mv | AT rezasobhani grayisometriesforfinitepgroups |