POSET METRICS ADMITTING ASSOCIATION SCHEMES AND A NEW PROOF OF MACWILLIAMS IDENTITY

Oh, Dong Yeol

doi:10.4134/JKMS.2013.50.5.917

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POSET METRICS ADMITTING ASSOCIATION SCHEMES AND A NEW PROOF OF MACWILLIAMS IDENTITY

Journal title : Journal of the Korean Mathematical Society
Volume 50, Issue 5, 2013, pp.917-931
Publisher : The Korean Mathematical Society
DOI : 10.4134/JKMS.2013.50.5.917

Title & Authors

POSET METRICS ADMITTING ASSOCIATION SCHEMES AND A NEW PROOF OF MACWILLIAMS IDENTITY
Oh, Dong Yeol;

Abstract

It is known that being hierarchical is a necessary and sufficient condition for a poset to admit MacWilliams identity. In this paper, we completely characterize the structures of posets which have an association scheme structure whose relations are indexed by the poset distance between the points in the space. We also derive an explicit formula for the eigenmatrices of association schemes induced by such posets. By using the result of Delsarte which generalizes the MacWilliams identity for linear codes, we give a new proof of the MacWilliams identity for hierarchical linear poset codes.

Keywords

MacWilliams identity;association scheme;poset code;poset metric;

Language

English

Cited by

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