A classification of posets admitting the MacWilliams identity

In this paper, all poset structures that admit the MacWilliams identity are classified, and the MacWilliams identities for poset weight enumerators corresponding to such posets are derived. It is proved that being a hierarchical poset is a necessary and sufficient condition for a poset to admit the...

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Veröffentlicht in:	IEEE transactions on information theory 2005-04, Vol.51 (4), p.1424-1431
Hauptverfasser:	Kim, H.K., Oh, D.Y.
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Classification Codes Coding, codes Exact sciences and technology Galois fields Hamming weight Hierarchical poset Information systems Information theory Information, signal and communications theory leveled Linear code MacWilliams identity Mathematics poset codes Signal and communications theory Sufficient conditions Telecommunications and information theory
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Beschreibung
Zusammenfassung:	In this paper, all poset structures that admit the MacWilliams identity are classified, and the MacWilliams identities for poset weight enumerators corresponding to such posets are derived. It is proved that being a hierarchical poset is a necessary and sufficient condition for a poset to admit the MacWilliams identity. An explicit relation is also derived between the P-weight distribution of a hierarchical poset code and the P~-weight distribution of the dual code.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2005.844067