Spherical Codes With Prescribed Signed Permutation Automorphisms Inside Shells of Low-Dimensional Integer Lattices
Year: 2024
Type: article
Abstract: Let$\textrm {S}(n,t,k)$be the maximum size of a code containing only vectors of the kth 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.
Authors: Mikhail Ganzhinov, Patric R. J. Östergård
Institution: Aalto University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,495
OpenAlex ID: W4402743115