Title :
A classification of posets admitting the MacWilliams identity
Author :
Kim, Hyun Kwang ; Oh, Dong Yeol
Author_Institution :
Dept. of Math., Pohang Univ. of Sci. & Technol., South Korea
fDate :
4/1/2005 12:00:00 AM
Abstract :
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.
Keywords :
dual codes; linear codes; MacWilliams identity; P-weight distribution; dual code; hierarchical poset; hierarchical poset code; poset weight enumerators; Galois fields; Hamming weight; Linear code; Mathematics; Sufficient conditions; Hierarchical poset; MacWilliams identity; leveled; poset codes;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2005.844067
