Orbit codes from forms on vector spaces over a finite field
type: Item
instance of: scholarly article
title: Orbit codes from forms on vector spaces over a finite field
zbMATH Open document ID: 1497.94175
author: Angela Aguglia
author: Giuseppe Marino
author: Francesco Pavese
author: Alessandro Siciliano
author: Antonio Cossidente
published in: Advances in Mathematics of Communications
publication date: 2022-01-24T00:00:00Z
review text: The authors establish new techniques for the construction of orbit codes in this paper. They construct different families of orbit codes in the vector spaces of the symmetric bilinear forms, quadratic forms and Hermitian forms on an \(n\)-dimensional vector space over the finite field \(\mathbb{F}_q\). And also these codes admit the general linear group as a transitive automorphism group. They point out that \(\mathrm{GL}(V)\) is a subgroup of \(\mathrm{GL}(\tilde V)\). In particular, \(\mathrm{GL}(V)\) acts on the forms by preserving the rank. The authors prove the existing result for \(n\geq 3\), as follows; ``The stabilizer of \(U_2\) in \(\mathrm{GL}(V)\) is \(S\times C\), where \(S\) is the Singer cyclic group of \(\mathrm{GL}(V)\) generated by \(\sigma\) and \(C\) is the cyclic group generated by \(\tau\)''. Particularly, the authors refer to a good number of material and present them as references perfectly.
reviewed by: P. Shakila Banu
Mathematics Subject Classification ID: 94B25
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 7461991
zbMATH Keywords: orbit code
zbMATH Keywords: constant dimension code
zbMATH Keywords: subspace code
MaRDI profile type: Publication
full work available at URL: amc.2020105
OpenAlex ID: W3071847929
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DOI: 10.3934/AMC.2020105
description: scientific article; zbMATH DE number 7461991