MacWilliams-type identities for fragment and sphere enumerators

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 P̌. The linear changes of variables appearing in the identities are explicit. So we obtain, for example, the P-weight distribution of C as the P̌-weight distribution times an invertible matrix which is a generalization of the Krawtchouk matrix. c © 2005 Elsevier Ltd. All rights reserved. MSC: primary 94B60; 11T71