On a MacWilliams type identity and a perfectness for a binary linear (\(n,n-1,j\))-poset code.
A MacWilliams type identity for the \(P\)-weight enumerator polynomial of the binary \(P\)-code and its dual, and the parameters of the binary linear perfect \(P\)-code are obtained; here \(P\) is an \((n,n-1,j)\)-poset, i.e. a partially ordered set of cardinality \(n\) with \(n-1\) maximal elements and \(j\) \((1\leq j\leq n-1)\) minimal elements. Furthermore, for an \((n,n-1,j)\)-poset \(P\) and for a chain \(P\) with \(n\) elements, a relation between the \(P\)-distance and \(P\)-weight of vectors in \(\mathbb{Z}^n_2\) is obtained.
scientific article; zbMATH DE number 1915537