Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914707106955264 |
|---|---|
| author | Mikhail, Ganzhinov J, Östergård Patric R. |
| author_facet | Mikhail, Ganzhinov J, Östergård Patric R. |
| contents | Let $\textrm{S}(n,t,k)$ be the maximum size of a code containing only vectors of the $k$th shell of the integer lattice $\mathbb{Z}^n$ such that the inner product between distinct vectors does not exceed $t$. In this paper we compute lower bounds for $\textrm{S}(n,t,k)$ for small values of $n$, $t$ and $k$ by carrying out computer searches for codes with prescribed automorphisms. We prescribe groups of signed permutation automorphisms acting transitively on the pairs of coordinates and coordinate values as well as other closely related groups of automorphisms. Several of the constructed codes lead to improved lower bounds for spherical codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04330 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices Mikhail, Ganzhinov J, Östergård Patric R. Combinatorics Metric Geometry Let $\textrm{S}(n,t,k)$ be the maximum size of a code containing only vectors of the $k$th shell of the integer lattice $\mathbb{Z}^n$ such that the inner product between distinct vectors does not exceed $t$. In this paper we compute lower bounds for $\textrm{S}(n,t,k)$ for small values of $n$, $t$ and $k$ by carrying out computer searches for codes with prescribed automorphisms. We prescribe groups of signed permutation automorphisms acting transitively on the pairs of coordinates and coordinate values as well as other closely related groups of automorphisms. Several of the constructed codes lead to improved lower bounds for spherical codes. |
| title | Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2403.04330 |