Jacobi forms over totally real fields and type II codes over Galois rings \(\operatorname{GR}(2^{m},f)\).
type: Item
instance of: scholarly article
title: Jacobi forms over totally real fields and type II codes over Galois rings \(\operatorname{GR}(2^{m},f)\).
zbMATH Open document ID: 1075.11039
published in: European Journal of Combinatorics
publication date: 2004-08-06T00:00:00Z
review text: In this paper, the authors study type II codes over Galois rings and their weight enumerators over an invariant polynomial ring of generalized Clifford-Weil group, as it has been done for codes over \(\mathbb{F}_{2^2}\). They use an algebra homomorphism to give a correspondance between Jacobi forms over totally real field and this invariant polynomial ring where weight enumerators belong. As an example, authors illustrate their results with a complete list of type II codes of length 4 over Galois ring of cardinality 16 and characteristic 4. Citations are well used and results are well presented highlighting the interest of the topic, type II codes over Galois rings of characteristic a power of 2 and their link with Jacobi modular forms.
Mathematics Subject Classification ID: 11F50
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 2082041
zbMATH Keywords: Invariant polynomial ring
zbMATH Keywords: generalized Clifford-Weil group
zbMATH Keywords: Galois ring
zbMATH Keywords: Jacobi form
zbMATH Keywords: totally real field
zbMATH Keywords: type II codes
author: Koichi Betsumiya
author: YoungJu Choie
MaRDI profile type: Publication
full work available at URL: j.ejc.2003.01.001
OpenAlex ID: W2050519401
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DOI: 10.1016/J.EJC.2003.01.001
description: scientific article; zbMATH DE number 2082041