J. Korean Math. Soc. 2013; 50(5): 917-931
Printed September 1, 2013
https://doi.org/10.4134/JKMS.2013.50.5.917
Copyright © The Korean Mathematical Society.
Dong Yeol Oh
Hanbat National University
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
MSC numbers: 05E30, 94B05
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