MacWilliams-type identities for fragment and sphere enumerators

Authors:
Dae San Kim
Affiliations:
Department of Mathematics, Sogang University, Seoul, Republic of Korea
Venue:
European Journal of Combinatorics
Year:
2007

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Abstract

Let P = n11⊕...⊕nt1 be the poset given by the ordinal sum of the antichains ni1 with ni elements. We derive MacWilliams-type identities for the fragment and sphere enumerators, relating enumerators for the dual C⊥ of the linear code C on P and those for C on the dual poset P. The linear changes of variables appearing in the identities are explicit. So we obtain, for example, the P-weight distribution of C⊥ as the P-weight distribution times an invertible matrix which is a generalization of the Krawtchouk matrix.