Orthogonal designs and Type II codes over \(\mathbb Z_{2k}\)
type: Item
instance of: scholarly article
title: Orthogonal designs and Type II codes over \(\mathbb Z_{2k}\)
zbMATH Open document ID: 0998.94020
DOI: 10.1023/A:1013804414889
author: Masaaki Harada
author: Christos Koukouvinos
author: Stelios D. Georgiou
published in: Designs, Codes and Cryptography
publication date: 2002-05-28T00:00:00Z
review text: The authors generalize known techniques using matrices to produce Type~I and Type~II codes over the ring \(\mathbb{Z}_{2k}.\) Type~II codes are self-dual codes such that all vectors have Euclidean weights congruent to 0 modulo \(4k\) and Type~I codes are self-dual codes that are not Type~II. They introduce two methods for constructing these codes using a generalization of orthogonal designs and compute several interesting examples of extremal codes. Type~II (resp. Type~I) real unimodular lattices are constructed from Type~II (resp. Type~I) codes, and several interesting examples of such lattices are also given.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B25
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 1746298
zbMATH Keywords: orthogonal designs
zbMATH Keywords: self-dual codes
zbMATH Keywords: Type~II codes over \(Z_{2k}\)
zbMATH Keywords: matrices
zbMATH Keywords: extremal codes
reviewed by: Steven T. Dougherty
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1746298