On a MacWilliams type identity and a perfectness for a binary linear (n,n−1,j)-poset code Original Research Article

For a (n,n−1,j)-poset P, which is a partially ordered set of cardinality n with n−1 maximal elements and j (1⩽j⩽n−1) minimal elements, we obtain a MacWilliams type identity for the P-weight enumerator polynomial of the binary linear P-code and its dual, and we find the parameters of the binary linear perfect P-code. Also, for a (n,n−1,j)-poset P and for a chain P with n elements, we get a relation between the P-distance and P-weight of vectors in Z2n.