Codes over \(\Sigma_{2m}\) and Jacobi forms over the quaternions
type: Item
instance of: scholarly article
title: Codes over \(\Sigma_{2m}\) and Jacobi forms over the quaternions
zbMATH Open document ID: 1068.94024
author: Steven T. Dougherty
author: YoungJu Choie
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 2004-12-17T00:00:00Z
review text: If \(i,j,k = ij\) denote the standard quaternions the authors consider the ring \(R=\mathbb{Z}/2m\mathbb{Z}+ i\mathbb{Z}/2m\mathbb{Z}+ j\mathbb{Z}/2m\mathbb{Z}+k\mathbb{Z}/ 2m\mathbb{Z}\), \(m\in \mathbb{N}\). They relate self-dual codes over \(R\) to quaternionic unimodular lattices and to self-dual lattices over \(\mathbb{Z}/2m\mathbb{Z}\). The connection is studied between the complete weight enumerators of codes over \(R\) and Jacobi forms on the half-spaces of quaternions (cf. the reviewer [\textit{A. Krieg}, Modular forms on half-spaces of quaternions (Lecture Notes in Mathematics 1143, Berlin, Springer) (1985; Zbl 0564.10032)]. Higher genus modular forms over the quaternions are also constructed using joint weight enumerators of codes.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 11H71
Mathematics Subject Classification ID: 11F50
zbMATH DE Number: 2123506
reviewed by: Aloys Krieg
MaRDI profile type: Publication
full work available at URL: s00200-004-0153-9
OpenAlex ID: W1965440796
DOI: 10.1007/S00200-004-0153-9
description: scientific article; zbMATH DE number 2123506