On a MacWilliams type identity and a perfectness for a binary linear (\(n,n-1,j\))-poset code.
type: Item
instance of: scholarly article
title: On a MacWilliams type identity and a perfectness for a binary linear (\(n,n-1,j\))-poset code.
zbMATH Open document ID: 1071.94023
DOI: 10.1016/S0012-365X(02)00624-6
author: Youngho Jang
author: Jeanam Park
published in: Discrete Mathematics
publication date: 2003-05-25T00:00:00Z
review text: A MacWilliams type identity for the \(P\)-weight enumerator polynomial of the binary \(P\)-code and its dual, and the parameters of the binary linear perfect \(P\)-code are obtained; here \(P\) is an \((n,n-1,j)\)-poset, i.e. a partially ordered set of cardinality \(n\) with \(n-1\) maximal elements and \(j\) \((1\leq j\leq n-1)\) minimal elements. Furthermore, for an \((n,n-1,j)\)-poset \(P\) and for a chain \(P\) with \(n\) elements, a relation between the \(P\)-distance and \(P\)-weight of vectors in \(\mathbb{Z}^n_2\) is obtained.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 68R15
zbMATH DE Number: 1915537
zbMATH Keywords: binary linear perfect poset code
zbMATH Keywords: MacWilliams identity
zbMATH Keywords: enumerator polynomial
zbMATH Keywords: dual code
zbMATH Keywords: extended binary Hamming code
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1915537