On codes that are invariant under the affine group.
type: Item
instance of: scholarly article
title: On codes that are invariant under the affine group.
zbMATH Open document ID: 1283.20001
published in: The Electronic Journal of Combinatorics
publication date: 2013-06-07T00:00:00Z
full work available at URL: v19i4p20
review text: Let \(k[V]\) be the space of functions from a finite vector space into the algebraically closure of its field of scalars. This paper concerns the vector space \(k[V]\) of functions from a finite vector space to an algebraically closed field of the same characteristic and its \(k\mathrm{AGL}(V)\)-submodules, the subspaces which are invariant under the natural action of the affine group \(\mathrm{AGL}(V)\). This paper gives an explicit description of the \(k\mathrm{AGL}(V)\)-submodules of \(k[V]\), using the standard coordinates on \(V\), as well as a combinatorial description of the lattice of submodules.
reviewed by: Nan Ji-Zhu
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 05E18
Mathematics Subject Classification ID: 51D25
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 6171803
zbMATH Keywords: invariant codes
zbMATH Keywords: lattices of submodules
zbMATH Keywords: affine groups
author: Peter Sin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6171803