On some self-dual codes and unimodular lattices in dimension 48
type: Item
instance of: scholarly article
title: On some self-dual codes and unimodular lattices in dimension 48
zbMATH Open document ID: 1071.94022
author: Masaaki Harada
author: Masaaki Kitazume
author: Akihiro Munemasa
author: B. Venkov
published in: European Journal of Combinatorics
publication date: 2005-05-04T00:00:00Z
review text: The shadow of a singly-even self-dual code is the coset of the code in the orthogonal of the doubly-even subcode. This subcode consists of two cosets of the doubly-even subcode. In certain cases, the union of one of these cosets and the subcode of doubly-even vectors can form a doubly-even self-dual code. The authors use this to show that one of the two doubly even self-dual neighbors of an extremal doubly even self-dual \([48,24,10]\) code whose shadow has minimum weight 4 is an extremal doubly even self-dual \([48,24,12]\) code. Similarly for lattices they show that every extremal odd unimodular lattice in dimension 48 whose shadow has minimum norm 2 has an extremal even unimodular neighbor. Additionally extremal singly even self-dual \([48,24,10]\) codes with shadows whose minimum weight is 8 and extremal odd unimodular lattices in dimension 48 whose shadows have minimum norm 4 are studied.
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 11H71
zbMATH DE Number: 2165399
zbMATH Keywords: self-dual codes
zbMATH Keywords: unimodular lattices
MaRDI profile type: Publication
full work available at URL: j.ejc.2004.06.013
OpenAlex ID: W1965294060
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DOI: 10.1016/J.EJC.2004.06.013
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description: scientific article; zbMATH DE number 2165399