MacWilliams-type identities for fragment and sphere enumerators

Dae San Kim
2007 European journal of combinatorics (Print)  
Let P = n 1 1 ⊕ · · · ⊕ n t 1 be the poset given by the ordinal sum of the antichains n i 1 with n i 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 posetP. The linear changes of variables appearing in the identities are explicit. So we obtain, for example, the P-weight distribution of C ⊥ as thě P-weight distribution times an invertible matrix which is a generalization of the Krawtchouk matrix.
doi:10.1016/j.ejc.2005.07.018 fatcat:4tp6dkgdf5gkrjuhxb3h5cnybe