Classification of Poset-Block Spaces Admitting MacWilliams-Type Identity

In this paper, we prove that a poset-block space admits a MacWilliams-type identity if and only if the poset is hierarchical, and at any level of the poset, all the blocks have the same dimension. When the poset-block admits the MacWilliams-type identity, we explicitly state the relation between the...

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Bibliographic Details
Published in:IEEE transactions on information theory 2012-12, Vol.58 (12), p.7246-7252
Main Authors: Pinheiro, J. A., Firer, M.
Format: Article
Language:English
Subjects:
Applied sciences
Block codes
Classification
Codes
Coding, codes
Exact sciences and technology
Information theory
Information, signal and communications theory
Linear code
MacWilliams identity
MacWilliams-type identity
Measurement
Polynomials
poset-block codes
Set theory
Signal and communications theory
Telecommunications and information theory
Transforms
Vectors
weight distribution
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Summary:In this paper, we prove that a poset-block space admits a MacWilliams-type identity if and only if the poset is hierarchical, and at any level of the poset, all the blocks have the same dimension. When the poset-block admits the MacWilliams-type identity, we explicitly state the relation between the weight enumerators of a code and its dual.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2012.2210192