Type II self-dual codes over finite rings and even unimodular lattices
type: Item
instance of: scholarly article
title: Type II self-dual codes over finite rings and even unimodular lattices
zbMATH Open document ID: 0958.94037
DOI: 10.1023/A:1018696102510
author: Steven T. Dougherty
author: T. Aaron Gulliver
author: Masaaki Harada
published in: Journal of Algebraic Combinatorics
publication date: 2000-02-03T00:00:00Z
review text: Self-dual codes over rings \({\mathbb Z}_k\) are studied, with special attention given to the case \(k=2^m\). A Type II code over \({\mathbb Z}_{2^m}\) is a self-dual code in which every codeword has Euclidean weight a multiple of \(2^{m+1}\). Such codes are shown to be related to self-orthogonal codes over \({\mathbb Z}_{2^{m+1}}\), and to even unimodular lattices, generalising a result of \textit{A. Bonnecazé, P. Solé} and \textit{A. R. Calderbank} [IEEE Trans. Inf. Theory 41, 366-377 (1995; Zbl 0822.94009)]. The existence of double circulant Type II codes over \({\mathbb Z}_{2^m}\) is considered and examples are given of extremal codes for \(m=3,4,5\).
Mathematics Subject Classification ID: 94B60
zbMATH DE Number: 1334703
zbMATH Keywords: self-dual code over finite ring
zbMATH Keywords: Type II code
zbMATH Keywords: double circulant code
zbMATH Keywords: even unimodular lattice
reviewed by: Patrick Fitzpatrick
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1334703