Codes over rings, complex lattices and Hermitian modular forms
type: Item
instance of: scholarly article
title: Codes over rings, complex lattices and Hermitian modular forms
zbMATH Open document ID: 1070.94024
author: YoungJu Choie
author: Steven T. Dougherty
published in: European Journal of Combinatorics
publication date: 2005-02-23T00:00:00Z
review text: The authors develop a theory of codes over the finite ring \(S_{2m} = {\mathbb Z}_{2m} + i{\mathbb Z}_{2m}\). They consider complete, symmetrized and complete joint weight enumerators of these codes and their duals. A connection between self-dual codes and complex unimodular lattices over the Gaussian integers \({\mathbb Z}[i]\) is studied. A theory of shadows for lattices and codes over \(S_{2m}\) is developed. A set of weight enumerators is used to construct Hermitian Jacobi forms and Hermitian modular forms.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B60
Mathematics Subject Classification ID: 11H99
Mathematics Subject Classification ID: 11F50
zbMATH DE Number: 2137545
zbMATH Keywords: self-dual codes
zbMATH Keywords: unimodular lattices
zbMATH Keywords: Hermitian modular forms
zbMATH Keywords: shadows
zbMATH Keywords: weight enumerator
reviewed by: Kanat Abdukhalikov
MaRDI profile type: Publication
full work available at URL: j.ejc.2004.04.002
OpenAlex ID: W1987911219
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cites work: Q4744337
cites work: Hermitian Jacobi forms
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cites work: Duality for modules over finite rings and applications to coding theory
DOI: 10.1016/J.EJC.2004.04.002
description: scientific article; zbMATH DE number 2137545